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Safety of Median Trees with Narrow Clearances on Urban Conventional Highways Phase III Final Report Submitted to: State of California Department of Transportation Traffic Operations Program Sacramento, CA 94273 Submitted by: Edward C. Sullivan, Principal Investigator Applied Research and Development Facility Cal Poly State University San Luis Obispo, CA 93407 March 2004 ABSTRACT This is the final report for the third phase of a Caltrans sponsored study to investigate the safety of placing large trees with narrow side clearance in medians of conventional state highways that also serve as principal urban streets. Although the study focused on trees in medians, the effects of many other roadside features were also considered. Previous phases of this study produced a literature search and contacts with experts in the field to identify and document what was already known about urban street trees and collisions. Data were then collected and analyzed for 65 conventional urban highway sections with medians, including facilities under both state and local jurisdiction, as well as with and without curbed medians. Statistical methods were used to explore quantitative relationships between both total collisions and fatal and injury ( F& I) collisions on these highway sections as influenced by various geometric, traffic and environmental conditions. The objective was to isolate the possible impacts of large median trees on collision rates and severity, and to determine the conditions that might mitigate or exacerbate any such impacts. The general conclusion of these initial investigations was that, for the highway sections considered, the presence of large median trees does consistently correlate with higher total accident rates, although differences observed in fatal and injury accident rates were generally not statistically significant. In addition, neither lower posted speeds nor increased side clearances to median trees were shown to be associated with reduced accidents. The detailed findings from this part of the investigation are provided in a separate Phase II report. 1 Phase III of the study dug further into the relationships found previously, and refined the study output in a number of important ways. First, the sites considered were limited to only highways under state jurisdiction and to only highways with curbed medians, in order to provide a more homogenous data set. In addition, the statistical modeling was modified to focus on collisions that occurred in or near the median area, as well as collisions located away from intersections. The data set was also expanded to include additional variables, including measured speeds and Caltrans rate group designations. Finally, additional model types not employed in Phase II were applied in the search for significant associations, and selected printed collision reports were examined in an effort to identify possible effects of trees not evident in the quantitative data. The conclusion of the Phase III investigation is that large trees planted in curbed medians along conventional urban and suburban state highways are associated with more collisions and with increased collision severity, however for some collision types the statistical associations are weak. The strengths of the associations found are summarized below. Strength of the Association Between Collisions and Median Trees in ⇒ Total # of Collisions # of F& I Collisions % of F& I Collisions Interior Lanes, Median Area & Beyond Significant Significant Significant Collision Locations Only Median Area & Beyond Weak Weak Significant Study findings show that increasing median width does not reduce collision expectations, and that the effects of speeds are mixed. 1 Safety of Trees with Narrow Clearances on Urban Conventional Highways: Phase II Final Report. Applied Research and Development Facility, Cal Poly State University. February 2003. Internet, on line at: http:// ceenve. calpoly. edu/ sullivan/ trees/. iii ACKNOWLEDGMENTS This report results from the efforts of an interdisciplinary team composed of the following faculty and students at Cal Poly State University: James Daly, Faculty Member, Statistics Karthikeyan Dhandapani, Graduate Assistant, Civil and Environmental Engineering Laine Elliott, Student Assistant, Statistics Brendon Finnecy, Student Assistant, Civil and Environmental Engineering Travis Hurt, Student Assistant, Civil and Environmental Engineering Eugene Jud, Faculty Member, Civil and Environmental Engineering Justin Link, Student Assistant, Civil and Environmental Engineering Danielle Ringstmeyer, Student Assistant, Civil and Environmental Engineering Edward Sullivan, Faculty Member, Civil and Environmental Engineering The study team was augmented by a panel of distinguished technical advisors: Professor Emeritus Ezra Hauer of the University of Toronto, Professor Emeritus Robert Layton of Oregon State University, and Professor Richard McGinnis of Bucknell University. We appreciate their valuable insights in the development of the study methodology and their comments regarding the draft final report. We appreciate the guidance and assistance of Phil Jang, the study’s technical monitor for Caltrans, of Mike Gray, Lyle Oehler, and Jack Boda, who provided suggestions and administrative assistance throughout the study, and of Janice Benton, of the Caltrans TASAS Unit, who helped us with many aspects of data collection. We are also very grateful for the help received from numerous other Caltrans headquarters and district office staff members throughout the state who helped us with suggestions and with assistance in data collection. Our additional thanks to dozens of local public works staff throughout California who assisted us in generously contributing their time and effort to provide needed traffic and roadway data. DISCLAIMER The contents of this report reflect the views of the authors who are alone responsible for the findings and accuracy of the information presented herein. The contents do not necessarily reflect the official views or policies of the State of California. The report does not constitute a standard, specification or regulation. iv Safety of Median Trees with Narrow Clearances on Urban Conventional Highways: Phase III Final Report TABLE OF CONTENTS ABSTRACT....................................................................................................................... ......... iii DISCLAIMER..................................................................................................................... ......... iv TABLE OF CONTENTS............................................................................................................... v LIST OF FIGURES...................................................................................................................... vi LIST OF TABLES........................................................................................................................ vi 1. Introduction and Executive Summary................................................................................... 1 1.1 Background..................................................................................................................... .. 1 1.2 Overview of Methodology................................................................................................. 3 1.3 Summary of Findings...................................................................................................... 10 1.4 Overview of the Rest of the Report................................................................................ 12 2. Development of the Phase III Data Set................................................................................ 13 2.1 Chapter Introduction....................................................................................................... 13 2.2 Sampling Considerations............................................................................................... 13 2.3 Coding of Highway Section Characteristics................................................................. 17 2.4 Coding of Collision Data................................................................................................. 19 3. Results from Modeling Based on TASAS Collision Data.................................................. 23 3.1 Chapter Introduction....................................................................................................... 23 3.2 Generalized Linear Modeling.......................................................................................... 23 3.3 Estimation of Simple Accident Rates............................................................................ 45 3.4 Tests for Differences in Collision Characteristics........................................................ 52 4. Results from Additional Investigations.............................................................................. 59 4.1 Chapter Introduction....................................................................................................... 59 4.2 Review of Selected Printed Collision Reports.............................................................. 59 4.3 Findings from Field Investigations of Collision Concentrations................................ 65 4.4 Investigation of Differences between Posted Speeds and Measured Speeds........... 73 4.5 The Modeling Implications of Differences Between SWITRS and TASAS................. 76 5. Conclusion and Recommendations.................................................................................... 81 Appendix A – Example Data for Study Sections with Median Trees.................................... 85 Appendix B – List of Study Sections without Median Trees................................................. 87 Appendix C – Section Photos.................................................................................................. 89 Appendix D – Photos of Intersections with Collision Concentrations................................ 93 v LIST OF FIGURES Figure 1. Printed Collision Reports  Breakdown of Median Types............................................ 60 Figure 2. Collisions Reports: Severity Breakdown by Median Type........................................... 61 Figure 3. Collisions Reports: Overall Collision Type Breakdown by Median Type..................... 61 Figure 4. Concentration of Collisions on 04 ALA 123 ( Berkeley)............................................... 67 Figure 5. Concentration of Collisions on 12 ORA 039 ( Buena Park).......................................... 67 Figure 6. Concentration of Collisions on 07 LA 066 ( Claremont)............................................... 68 Figure 7. Concentration of Collisions on 04 ALA 238 ( Hayward)............................................... 68 Figure 8. Concentration of Collisions on 12 ORA 039 ( Huntington Beach)................................ 69 Figure 9. Concentration of Collisions on 07 LA 066 ( La Verne)................................................. 69 Figure 10. Concentration of Collisions on 04 SM 081 ( South San Francisco)........................... 70 Figure 11. Measured Distances from End of Median to First Tree............................................. 71 Figure 12. SR 123 at Addison St. ( Berkeley) ( 15 m. to First Median Tree)................................ 72 Figure 13. SR 66 at Indian Hill Blvd. ( Claremont) ( 35 m. to First Median Tree).......................... 72 Figure 14. SR 66 at East Mountain ( Claremont)......................................................................... 73 Figure 15. SR 66 at Towne Ave. ( Claremont)............................................................................. 73 Figure 16. Comparison of Posted Speeds and 85% ile Speeds.................................................. 75 Figure 17. Comparison of Posted Speeds and Top of Pace Speeds......................................... 76 LIST OF TABLES Table 1. The Study Data Set at a Glance..................................................................................... 4 Table 2. Principal Highway Characteristics Considered in the Phase III Study............................ 6 Table 3. Average Characteristics of Highway Sections with and without Median Trees.............. 7 Table 4. Collision Characteristics Considered in the Phase III Analysis....................................... 7 Table 5. MVM of Exposure by Posted Speeds, ADT, and Median Trees................................... 14 Table 6. MVM of Exposure by Posted Speeds Combined with ADT, and Median Trees........... 14 Table 7. MVM of Exposure by Median Width and Setback to Median Trees.............................. 15 Table 8. MVM of Exposure by Median Width Combined with Speed, and Median Trees........... 15 Table 9. MVM of Exposure by Speed and ADT Combined with Setback to Median Trees........ 16 Table 10. MVM of Exposure by Rate Group Combined with Median Width, and Median Trees16 Table 11. MVM of Exposure by Rate Group Combined with ADT Category, and Median Trees17 Table 12. Coding of Highway Section Characteristics................................................................ 17 Table 13. Significance of Initial Models for All “ No Right Side” Collisions.................................. 25 Table 14. Significance of Initial Models for F& I “ No Right Side” Collisions................................ 26 Table 15. Significance of Initial Models for All “ Left Side Only” Collisions.................................. 28 Table 16. Significance of Initial Models for F& I “ Left Side Only” Collisions................................ 29 Table 17. Summary of Multivariate Models with Intersection Collisions Included....................... 31 Table 18. Summary of Multivariate Models with Intersection Collisions Excluded..................... 33 vi Table 19. Multivariate Model GL 1 A Estimated for NRS ALL Collisions.................................... 34 Table 20. Multivariate Model GL 1 B Estimated for NRSNI ALL Collisions................................ 35 Table 21. Multivariate Model GL 1 C Estimated for NRSNI ALL Collisions................................ 36 Table 22. Multivariate Model GL 1 D Estimated for NRSNI ALL Collisions................................ 36 Table 23. Multivariate Model GL 1 E Estimated for NRS F& I Collisions.................................... 37 Table 24. Multivariate Model GL 1 F Estimated for NRS F& I Collisions..................................... 37 Table 25. Multivariate Model GL 1 G Estimated for NRS F& I Collisions.................................... 38 Table 26. Multivariate Model GL 2 A Estimated for NRS ALL Collisions.................................... 39 Table 27. Multivariate Model GL 2 B Estimated for NRS F& I Collisions.................................... 40 Table 28. Multivariate Model GL 2 C Estimated for LSO ALL Collisions.................................... 40 Table 29. Multivariate Model GL 2 D Estimated for LSO F& I Collisions..................................... 41 Table 30. Multivariate Model GL 3 A Estimated for LSO Collisions........................................... 41 Table 31. Multivariate Model GL 3 A Re Estimated Without Section 08 SB 083....................... 42 Table 32. Multivariate Model GL 3 B Estimated for LSONI Collisions........................................ 43 Table 33. Multivariate Model GL 3 C Estimated for NRSNI Collisions....................................... 43 Table 34. Multivariate Model GL 3 D Estimated for NRSNI Collisions....................................... 43 Table 35. Left Side Accident Rates Stratified by Presence/ Absence of Median Trees.............. 46 Table 36. Left Side Accident Rates Stratified by Rate Group..................................................... 47 Table 37. Left Side Accident Rates Stratified by Average Daily Traffic...................................... 48 Table 38. Left Side Accident Rates Stratified by 85% ile Speed................................................. 49 Table 39. Left Side Accident Rates Stratified by Posted Speed................................................. 49 Table 40. Left Side Accident Rates Stratified by Number of Directional Lanes.......................... 50 Table 41. Left Side Accident Rates Stratified by Median Width................................................. 50 Table 42. Left Side Accident Rates Stratified by Setback to Median Trees............................... 51 Table 43. Left Side Accident Rates Stratified by Tree Trunk Diameter...................................... 52 Table 44. Comparison of Overall Collision Types for All Collisions............................................ 53 Table 45. Comparison of Overall Collision Types for Fatal and Injury Collisions....................... 54 Table 46. Comparison of Objects Hit for Collisions in the “ Left Side Only” Data Set................. 54 Table 47. Comparison of Collision Types for All Left Side Collisions by Posted Speed............. 55 Table 48. Comparison of Collision Types for F& I Left Side Collisions by Posted Speed........... 55 Table 49. Surface Conditions for Left Side Collisions with and without Median Trees............... 56 Table 50. Lighting Conditions for Left Side Collisions with and without Median Trees............... 56 Table 51. Violations Cited for Left Side Collisions with and without Median Trees.................... 56 Table 52. Number of Parties Involved for Left Side Collisions with and without Median Trees.. 57 Table 53. Collision Statistics Used to Screen Collision Concentrations for Further Investigation................................................................................................................ 66 Table 54. Coverage of Available Speed Zone Study Data......................................................... 74 Table 55. Comparisons of TASAS and SWITRS Data Sets for Equivalent Highway Sections... 77 vii 1. Introduction and Executive Summary 1.1 Background The California Department of Transportation ( Caltrans) Traffic Operations Program asked California Polytechnic State University ( Cal Poly) to perform a study of the safety of trees with limited side clearance in medians of urban and suburban conventional highways. The study was motivated by the need to develop a better empirical foundation on which to base agency policy for responding to local community requests for planting additional median trees. The study focused on estimating statistical associations between the number and severity of collisions and the presence of median trees. The influence of many other design and environmental features were also taken into consideration. The overall study was conducted in three phases, funded and conducted sequentially: Phase I – An investigation to determine what was already known about traffic safety and urban street trees, using the techniques of literature search and contacts with pertinent organizations and experts. In addition, this phase established the technical approach to the work conducted in Phase II. Phase II – An initial statistical investigation of broad cross sectional relationships between collision experience and the presence of trees in urban and suburban conventional highway medians. The purpose was to see if significant differences in collision experience are statistically associated with the presence of median trees and, if so, to identify the factors that might mitigate or exacerbate that association. The results of the Phase I and Phase II investigations appear in an earlier report. 2 Phase III – Further in depth investigations, primarily of a cross sectional statistical modeling nature, to refine and extend the data set and modeling of Phase II, and to address certain unanswered questions that remained at the close of the earlier investigation. This is the final report for Phase III of the study. It extends but does not supercede the Phase II report issued previously. The Phase III investigation, which is the subject of this report, addressed collision experience for the following highway types: Highways in urban and suburban settings that serve a mix of through and local access traffic ( rural highways were not considered). Conventional highways, that is, highways without access control except as determined by local land development practices. Highways within the state highway system, owned and managed by the California Department of Transportation. Highways likely to be viewed as local arterials ( as opposed to collectors or locals). Highways with curbed raised medians, both with and without median trees ( to permit comparison). 2 Safety of Trees with Narrow Clearances on Urban Conventional Highways: Phase II Final Report. Applied Research and Development Facility, Cal Poly State University. February 2003. Internet, on line at: http:// ceenve. calpoly. edu/ sullivan/ trees/. For these highway types, site characteristics, such as roadway widths, lane widths, median widths, setbacks, traffic volumes, speeds, and surrounding development types, vary widely. The State’s TASAS3 data system was used to identify all highway sections in the California highway inventory with the desired combinations of physical characteristics. Suitable candidate sections were defined as highway sections matching the above criteria, where geometric characteristics and other relevant road conditions remain mostly unchanged for about a mile or more. It was felt that study sections needed to be at least about a mile long in order to avoid excessive random variation in collision experience relative to the average. The suitability ( that is, the homogeneity) of each apparently suitable candidate study section was verified by a site visit during which numerous site measurements were obtained. These site visits resulted in eliminating some locations that were unsuitable due to lack of homogeneity or other apparent reasons. In a few cases, additional highway sections with suitable characteristics were discovered during the site visits. Some candidate sections were subsequently eliminated for other reasons, for example where we later determined that median trees were planted too recently to match the coverage period of the collision data. The final Phase III data set, created by combining new section data with suitable state highway sections remaining from Phase II, contains nineteen state highway sections with large median trees and ten state highway sections with raised curbed medians without trees. “ Large” trees are defined as trees with trunk diameters 100 mm ( 4 inch) or more at a point 1.2 m. ( 4 feet) above the ground. The final data set contains most of the potentially suitable candidate state highway sections in California of sufficient length, and virtually all of the suitable candidate sections within the major urban areas of Northern and Southern California ( Caltrans Districts 04, 07, 08, 11, and 12). A small number of potentially suitable sections located in the Central Valley and far north in the San Francisco Bay Area were not included due to travel inconvenience and the belief that the highway sections already available were a sufficiently large and representative data set for the intended analysis. Note that two of the nineteen median tree sections with posted speeds of 50 mph or more were excluded from most of the statistical analyses, since they were considered not entirely representative of the highway types of interest. Collision data were obtained for all study sections for the six year period from January 1996 through December 2001. Analogous to the one mile minimum adopted for section length, six years was considered an appropriate period to eliminate excessive random variation in the collision data. Local authorities were contacted to determine that for all the candidate sections with median trees, the trees had been in place at least since 1996. The corresponding traffic volumes for each section were obtained from a Caltrans web site, 4 and field measurements of vehicle speeds were obtained, where available, from the Caltrans district offices. Adequate field speed data to characterize traffic conditions during 1996 2001 were available for 27 of the 29 highway sections in the final data set. An extensive statistical analysis was undertaken, using several different model forms to examine the possible relationships between collisions, the presence of nearby “ large” trees, and other roadway, traffic, and environmental characteristics. The statistical analysis examined relationships in both the number and severity of collisions. One can hypothesize that, all else being equal, the number of collisions might be affected by median trees because nearby trees may restrict visibility, especially at intersections, or because driver behavior and surface friction might be affected by shadows or detritus on the road surface. One can also hypothesize that 3 TASAS = Traffic Accident Surveillance and Analysis System. 4 At http:// www. dot. ca. gov/ hq/ traffops/ saferesr/ trafdata/ 2 severity might be affected because large trees are unyielding fixed objects, consistently shown to be among the most harmful of all roadside objects to hit. On the other hand, there may also exist countervailing positive safety benefits from trees due to traffic calming, reduction of glare, blocking of cross median collisions, and control of runoff and erosion. Although this study addressed many relationships between median street trees and traffic safety, some things were not considered. For example, the study did not directly consider the increased risks to road crews in maintaining median vegetation, other maintenance costs that might result due to pavement damage from root growth, or possibly enhanced pavement life from shading. This study was never intended to provide a comprehensive benefit cost assessment of all aspects of planting median trees along urban and suburban conventional state highways. Rather, it is a focused examination of the safety consequences of median trees, based on a substantial data set of historical collision data. It should be noted that the statistical models developed in this study are strictly cross sectional. They estimate how differences in roadway characteristics, with and without median trees, are related to differences in accident rates by comparing similar but different highway sections. While before after comparisons of particular highway sections could provide substantial additional insights, time constraints and data limitations did not accommodate making before after site specific comparisons. Finally, it should be noted that our data set consists entirely of urban and suburban roadway sections in large urban areas of California. Thus, these findings are not necessarily applicable to the design types and driver populations found elsewhere. The following sections provide an overview of the study methodology and a summary of the principal findings. The details of the work are presented in the other chapters and appendices. 1.2 Overview of Methodology The principal methodology for Phase III of this study was to apply a variety of statistical modeling approaches to examine relationships between collisions, median trees, and other roadway characteristics. In addition, several parallel investigations of a non modeling nature were performed to produce additional insights into the problem at hand. The study methodology was motivated and informed by findings from the literature review and contacts with experts in the field. The literature review, from Phase I of the study, shows that while it is well established for rural highways that unprotected trees near the traveled way substantially increase collisions and their severity, there is little direct empirical evidence on this issue available for urban and suburban conventional arterials. What little evidence does exist presents conflicting conclusions. The specific components of the methodology for this study are: Expanded data collection for study sections on state highways. Statistical Modeling: • Generalized linear modeling of relationships between total and fatal and injury ( F& I) collisions and roadway characteristics ( three distinct model structures were applied), • Estimation and comparison of simple accident rates and their confidence intervals, • Tests of differences in collision characteristics, with and without median trees. Supplemental Investigations: • Review of selected original collision reports – narratives and other details, • Field investigations of possible visibility limitations near selected collision clusters, 3 • Examination of differences in posted speeds and measured speeds for the selected highway sections, and their implications for statistical modeling, • Assessment of differences in collision data between TASAS and SWITRS ( as follow up to Phase II). The data collection plan was guided by the need to have acceptable statistical properties for the accident models to be developed. We used a rule of thumb that we should seek at least 250 million vehicle miles ( MVM) of exposure for key combinations of the principal section variables of concern, specifically median type ( trees or no trees) combined with the rate group, the posted speed, and the median width category. The 250 MVM threshold would permit us to estimate the overall fatal and injury accident rates in each category within about a 12.5% expected error at 95% statistical confidence. 5 Table 1. The Study Data Set at a Glance State Highways With Median Trees Without Median Trees Total Number: 19 10 29 Sections: Total Mileage 40.5 17.8 58.3 MVM of exposure ( in 6 yrs.) 3268 2055 5323 Total 10563 3720 14283 Fatal & Injury 4334 1746 6080 All Collisions: Fatal 34 14 48 Total 6826 2761 9587 Fatal & Injury 2998 1384 4382 Right Side Collisions Eliminated: Fatal 29 14 43 Total 1648 706 2354 Fatal & Injury 759 396 1155 Left Side ( Median) Collisions Only: Fatal 7 5 12 Total 4328 1842 6170 Fatal & Injury 1865 859 2724 Right Side & Intersection Collisions Eliminated: Fatal 22 9 31 Total 597 242 839 Fatal & Injury 265 125 390 Left Side ( Median) Collisions Only; No Intersections: Fatal 3 2 5 5 95% statistical confidence is widely used in exploratory statistical studies of this nature. A higher level, say 99%, would result in fewer comparisons being judged statistically significant; a lower level would result in more comparisons being judged significant. 4 Upon applying the various selection criteria, twenty nine California state highway sections were identified with which to perform the Phase III statistical analysis. The overall features of these twenty nine sections are summarized in Table 1 above. Table 1 shows that there are nearly twice as many sections with median trees as without trees, and more than twice the mileage; however, the sections with median trees have only about 60% more exposure ( MVM) than the sections without trees. This reflects the fact that, on average, the sections without trees have more traffic ( the average ADT is 36,150 for sections with median trees compared to 49,127 for sections without). There are also many other differences among the characteristics of the twenty nine sections, and in their collision experience. Table 1 also shows collision counts for the six year analysis period, broken down by total collisions, fatal and injury ( F& I) collisions, and fatalities only. Collision counts are further grouped by where on the highways the collisions occurred. Of the five sets of counts shown, the first set includes all reported collisions on the state highway sections as reported in the State’s TASAS database. 6 The second set excludes collisions described as occurring entirely on the right side of the highway, defined as the right lane, the right shoulder, or beyond. The third set is more selective; including only collisions having some reported impact in the left ( median) shoulder area, the median, or beyond. The fourth and fifth data sets are the same as the second and third, except collisions located at intersections are not included. The statistical modeling for Phase III focused entirely on the second through fifth data sets, excluding collisions occurring entirely on the right side. Initially, whether or not to include collisions at intersections was questioned. On the one hand, collisions typically cluster at intersections where operations are dominated by factors related to accommodating turning conflicts. This argues for ignoring intersection collisions. On the other hand, if median trees are planted close to intersections, they might impact sight distances and, consequently, collision experience. Although investigations made during the study show that intersection sight distances are generally not restricted by median trees for the highways in our data sets, it was decided to perform statistical modeling both with and without intersection collisions. A quick look at Table 1 suggests that the presence of trees in medians is not associated with dramatic differences, although some differences are evident. Of 2354 left side collisions in the data set, only 12 are fatalities, although nearly 50% ( 1143) involve injuries. While sections with median trees represent 69% of the total mileage and 61% of the total exposure ( MVM), 58% of the left side fatalities occurred on sections with median trees. 7 On the other hand, 66% of the injury collisions and 70% of all left side collisions occurred on sections with median trees. If intersection collisions are excluded, 68% of the left side injury collisions and 71% of all left side collisions occurred on sections with median trees. Clearly, the possible associations between median trees and the number of accidents, and the injury accidents in particular, warrant in depth investigation. This report examines these associations in detail and assesses their statistical significance. In reading the findings of this analysis, it is important to recognize, as shown in Table 1, that the magnitude of the consequence in terms of increased collisions, especially increased fatal and injury collisions, is fairly small. This is noteworthy because, as mentioned previously, the highway sections in our data set represent the majority of urban 6 Collisions reported as occurring on cross streets near but not on the actual state highway were eliminated. 7 As small numbers, fatality percentages are highly variable – for example, one additional fatality in a section with trees would result in 61% of fatal collisions being on sections with trees. 5 conventional state highway sections in California of substantial length that have curbed medians. Information was coded for numerous physical, traffic, and environmental characteristics of highway sections thought potentially to be related to differences in their collision experience. Several additional data items, tested and found to be insignificant in the Phase II analysis, also appear in the data set but were generally not used in this part of the study. The principal characteristics considered in the Phase III statistical analysis are listed in Table 2 below. Table 2. Principal Highway Characteristics Considered in the Phase III Study Median Trees or Not# Section Length Average Daily Traffic Posted Speed Average Speed Critical ( 85% ile) Speed Top and Bottom of Pace Speed Range % Observations in 10 mph Pace Range Number of Lanes Rate Group Total Median Width Median Curb Height Median Shoulder Width Setback – Curb to Median Trees Setback – Traveled Way to Median Trees Median Tree Trunk Diameter Regularity of Median Tree Alignment# Right Curb Height Right Shoulder Width Right Side Trees or Not# Setback – Curb to Right Side Trees Right Side Utility Poles or Not# Right Side Parking or Not# Right Side Sidewalks or Not# Highway Curvature# Highway Grades# # 1 Lane Width Right Lane Width Adjacent Land Use# Cross Street Density# # Coded only as category variables, such as High/ Medium/ Low, Yes/ No, etc. Other derivative variables were generated during the analysis, usually by transforming continuous variables, such as ADT, median width, etc., to categorical variables in order to avoid having to make inappropriate assumptions regarding the linearity of their effects. As noted, the study objective was to try to determine conclusively whether or not the presence of large median trees is systematically associated with differences in the number or the severity of collisions on conventional urban highways. This was done primarily by comparing statistical associations for the sections with and without median trees. However, it should be noted that the selected highway sections also differ in other ways, which might also be associated with differences in their collision experience. Some of these differences are shown below in Table 3. A goal of statistical modeling is to try to sort out the differences associated with the characteristic of interest ( median trees) from any differences due to other factors, however this cannot always be done completely. Collision characteristics extracted from the statewide TASAS data base for each highway section are shown below in Table 4. As previously noted, these characteristics were extracted for five different data sets of collisions: ( 1) all collisions that occurred on the highway section; ( 2) all collisions except those involving only the right side of the highway; ( 3) all collisions involving only the median shoulder or beyond; ( 4) collisions excluding those located only on the right side of the highway or at intersections; and ( 5) collisions involving only the median shoulder or beyond and that are not at intersections. 6 Table 3. Average Characteristics of Highway Sections with and without Median Trees Section Characteristic Average for the 19 Sections with Median Trees Average for the 10 Sections without Median Trees Section Length ( miles) 2.7 1.8 Posted Speed ( mph) 38.4 40.5 85% ile Speed ( not all sections) 41.9 44.0 2001 Average Daily Traffic 36,774 50,459 Number of Directional Lanes 2.1 2.8 Median Width ( feet) 22.0 14.2 Median Shoulder ( feet) 0.7 0.5 Median Curb Height ( inches) 6.1 6.0 # 1 ( Median) Lane Width ( feet) 11.9 11.2 Right side Shoulder ( feet) 6.9 6.6 Six Year Exposure ( MVM) 172 206 Table 4. Collision Characteristics Considered in the Phase III Analysis Six Year Collision Counts: Total Collisions, Injury Collisions, Fatal Collisions Collision Type: Hit Object, Head On, Rear End, Sideswipe, Broadside, Hit Pedestrian# Object Struck: Tree, Sign or Pole, Guardrail or Barrier, Curb or Island# Violation: Under Influence, Following Too Close, Speeding# Surface Condition: Dry, Slippery, Wet, Snow or Ice# Road Condition: Nothing Unusual, Holes/ Ruts, Loose Material, Construction Reduction# Weather: Clear, Cloudy, Rain, Fog# Lighting: Daylight, Dusk, Darkness# # Separate breakdowns were produced for all accidents in the group, and for fatal and injury accidents independently. Appendices A and B show additional details about the highway section data set. The complete study data set is available on line at: http:// ceenve. calpoly. edu/ sullivan/ trees/ Statistical modeling was performed using SAS ( the Statistical Analysis System) and Excel. This included three types of generalized linear modeling, calculation of simple accident rates ( for total and fatal & injury collisions), and chi square tests of differences in collisions characteristics. Three forms of generalized linear models were tested with a wide range of candidate explanatory variables. These three model forms are shown below. In the equations, COLLi is 7 the observed annual number of collisions on highway section i; 8 Li is the section length; ADTi is the section average daily traffic; MEDTREEi is either 0 or 1, indicating whether section i has median trees; ε is the base of the natural logarithms (≈ 2.718); Xi1, Xi2, etc. are other section characteristics taken from Table 2; β0, β1, β2, etc. are parameters obtained from fitting the model to the data; and ERRi is the error term accounting for random effects not explicitly considered in the model. Model GL 1: iXXMEDTREEADTLiERRCOLLiiiii)(... 25143210++++++= ββββββε ( this error term ERRi is assumed to follow the negative binomial distribution) Model GL 2: iXXMEDTREEiiiERRADTLCOLLiii)(... 231210++++= ββββε ( this error term ERRi is assumed to follow the Poisson distribution) Model GL 3: iXXMEDTREEALLiIFiERRCOLLCOLLiii)()(... & 231210++++= ββββε ( this error term ERRi is assumed to follow the Poisson distribution) Models GL 1 and GL 2 were used to establish possible associations between the number of collisions in one of the five collision data sets and various section characteristics. For these models, some included all collisions, while others included fatal and injury only. Model GL 1 is considered a superior specification because it can capture the potential differences in collision experience associated with differences in the section ADT. Model GL 2, which is algebraically equivalent to modeling the section accident rate, is included for continuity with the work completed in Phase II. Model GL 3 is designed to examine accident severity, expressed as the proportion of fatal and injury collisions on each section. Simple accident rates were also estimated and compared. Since accident rates are generally based on simple stratifications and ignore possible relationships to section lengths and ADT levels, this approach is inherently inferior to multivariate modeling. However, as long as the limitations are recognized, accident rates are easily understood and potentially able to provide useful insights. Accident rates for all collisions and for F& I collisions in each of the five data sets were calculated separately for highway sections stratified by various characteristics, with and without median trees, using the following expression: () ΣΣΣΣ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛ = iyiyyiiyiyADTNLAR610 where: R is the average accident rate ( accidents per million vehicle miles), Aiy is the number of collisions observed on section i in year y, Li is the length ( in miles) of section i, Ny is the number of days of accident counts in year y ( usually 365), 8 In some models, COLLi and ADTi are the actual annual values for the six year observation period while, in other models, COLLi and ADTi are averages for the entire six year period. 8 ADTiy is the average daily traffic, in vehicles per day, for section i in year y, 106 is a scaling factor so R is in accidents per million vehicle miles ( MVM). Accident rates are presented with estimated 95% (±) confidence intervals obtained from: MVMR96.1=± where: MVM is the exposure in millions of vehicle miles associated with the estimated accident rate ( the denominator of the previous expression divided by the 106 scaling factor) The confidence interval formula follows directly from assuming that the number of collisions is a random variable that follows the Poisson distribution. Finally, chi square tests were used to explore if distributions of collision characteristics are significantly different with and without the presence of median trees, and with variations in other section characteristics. The corresponding test statistic is: () Σ− = kkkkEEO22χ where: χ2 is the Chi Square test statistic, Ok is an observed collision count within the distributions being compared, Ek is the corresponding expected count assuming both distributions match in their row and column totals. A large enough value of the test statistic χ2 allows us to reject the null hypothesis that the two distributions of collision characteristics are not significantly different. The methodologies used to carry out the four additional non modeling investigations conducted during Phase III were as follows: 1. The collision data for our highway sections were filtered in order to identify a subset of approximately 100 collisions that appeared especially important with regard to the possible influence of median trees. Targeted collisions were those involving incursion into the median shoulder or beyond, and one or more of the following: a fatality was involved. a tree or other median vegetation was hit, a pedestrian was hit, another vehicle was hit head on. Since the number of collisions with these specific characteristics was limited, some additional left side collisions were randomly selected from cases where injuries or where hitting posts and poles were involved. Caltrans district offices provided photocopies of the original collision reports for these selected collisions, and these reports were carefully scrutinized to understand the role of median trees with regard to their possible influence on each collision and its severity. 2. The collision data for our highway sections with trees were analyzed to identify noteworthy collision clusters. These clusters usually occurred in the vicinity of intersections. Selected 9 locations were re visited to make sight distance measurements, in order to see if visibility problems were evident and, if so, whether the presence of trees might be related. 3. Phase II of the study developed a number of statistical models that, for convenience, were based entirely on section posted speeds. In Phase III, measured section speed data were obtained and key speed measurements, such as critical ( 85% ile) speed and top of pace speed, were also used in the statistical modeling. A question remaining from Phase II is whether the use of actual speeds would make much difference in the findings. Consequently, an investigation was performed to compare section posted speeds with measured speeds, and to interpret any differences with respect to their implications for collision modeling. 4. The Phase II statistical modeling was based on 65 highway sections, including portions of state highways and local facilities considered to have similar characteristics. In order to do this, it was necessary to use two different sources of collision data: the TASAS data base for the state highway sections, and the California Highway Patrol’s SWITRS data base for the local facilities. 9 Although there is much similarity in the data in these two data systems, there are also some differences that raised concern that the findings of the Phase II modeling could have been impacted by inconsistencies in the two data sets. Consequently, an additional investigation was performed to assess the differences in the TASAS and SWITRS data sets for a number of selected state highway sections, and to explore the implications of any differences for the previously developed Phase II models. The major findings of these analyses are summarized in the following section. The results are documented in detail in the later chapters of this report. 1.3 Summary of Findings The principal conclusion from Phase III of this study is that large trees planted in curbed medians along conventional urban and suburban state highways are associated with more total collisions and more fatal and injury collisions, at the 95% level of statistical confidence, when collisions occurring only on the right side of the highway are excluded from consideration. In addition, collision severity ( measured by the proportion of F& I collisions) is significantly higher in the presence of median trees. When collisions are further limited to only those involving the median shoulder, the median, or beyond, a significant association continues to be found between the presence of median trees and severity. However, one highway section in the data set with an unusually high proportion of F& I collisions probably contributes disproportionally to the strength of this association. Only weak associations were found between median trees and the frequency of left side collisions. Nevertheless, based on all the evidence, we conclude that some association does exist between left side collisions and median trees. These findings hold across a wide range of highway types, including posted speeds ranging from 35 to 45 mph and a variety of median widths. These findings generally hold whether or not collisions occurring at intersections are included. In presenting these findings, we should clarify that “ significant” means “ statistically significant at the 95% confidence level.” A difference is regarded as statistically significant if it would appear less than 5% of the time due to random variation in the sample data, when in reality no difference would exist if we used the data for 100% of the highways of concern ( not just a 9 SWITRS = Statewide Integrated Traffic Records System, while TASAS = Traffic Accident Surveillance and Analysis System. 10 sample of them). When a difference is found not to be statistically significant, it is not proof that the difference in question does not exist. Rather, it means that the data do not support with 95% confidence the conclusion that the difference exists. Statistical methods of this type cannot demonstrate conclusively that something does not exist. In addition, we should recognize that differences found not to be significant at the 95% confidence level are sometimes statistically significant at lower confidence levels. 10 While the presence of median trees is generally associated with increased accidents and greater severity, other characteristics of the highway sections interact in complex and sometimes unexpected ways. Specifically, it was found that the number of collisions and collision severity usually decrease in association with lower actual ( 85% ile) section speeds but, in most cases, collisions increase in association with lower posted speeds. While simple accident rates are usually higher in the presence of median trees, the increase in accident rates is less for sections with 40 45 mph 85% ile speeds than for sections with 35 40 mph speeds. It was also found, counter intuitively, that the number of collisions and collision severity are associated with wider medians. However, no systematic relationship was found between the magnitudes of simple accident rates and median widths or setbacks to median trees. Estimates of simple accident rates show that overall accident rates for sections with median trees are in most situations significantly higher than overall rates for sections without trees. However, for most comparisons, the F& I accident rate differences are not statistically significant or are marginally significant. This result was found whether or not collisions occurring at intersections are included. The presence of median trees was also shown to be associated with statistically significant differences in collision characteristics. For most combinations of highway types, we observed increased proportions of hit object collisions and decreased proportions of head on and broadside collisions in the presence of median trees. While hit object collisions increase compared to other collision types, hit tree collisions increase relatively more, while other hit object types relatively decrease. There also exists an apparent association between median trees and the proportions of hit pedestrian collisions, especially for collisions not at intersections. All of the statistical analysis of this study involved cross sectional comparisons among similar groups of highway sections. No before after comparisons were made, although before after comparisons are recommended for future consideration, if found to be practical. Cross sectional models can give a general indication of what may occur if median trees are planted or removed at a particular site, if the site characteristics closely match the section data considered in the analysis. However, particular sites will always have unique features that limit the applicability of such models for prediction. The relationships developed in this report are not intended for predicting changes in collisions that might accompany some particular highway change. They were developed solely to determine whether or not significant statistical associations exist between collisions and the presence of median trees. An in depth investigation of about a hundred printed collision reports provided interesting and varied observations. The proportion of serious injuries and fatalities in collisions involving median trees appears about the same as in other hit object collisions in the sample. In just under half of the tree hit collisions examined, if the trees had not been present or had been cushioned in some manner, the resulting injuries would probably have been substantially 10 Although 95% can be said to be an arbitrary confidence level, it is widely regarded as an appropriate threshold in statistical investigations of this nature. 11 reduced. In about the same number of collisions, if the trees had not been present, the outcome may well have been more severe. The collision reports suggested no apparent linkage between the severity of hit tree collisions and median width. Some of the most serious tree hit collisions in the sample occurred on wide medians with substantial setback distances. Our investigation of differences between actual measured speeds and posted speeds on our selected highway sections revealed that although these measures are highly correlated, measured speeds ( for example, the 85% ile speeds) vary enough compared to posted speeds that, in an ideal world, measured speeds should be used in modeling. However, the data coverage for measured speeds is limited, affecting their ability to represent actual conditions on the highway. Consequently, using both measured speeds and posted speeds seems advisable. It was found that differences between the TASAS and SWITRS data used in the Phase II modeling lead to several kinds of biases in the collision counts obtained from these two data systems. However, these biases appear not to affect the ability of these models to estimate the associations between collisions and the presence of median trees. The findings of Phase II of this study are, on the whole, consistent with the findings presented in this report. The conclusions of the current study are more definitive due to the more in depth nature of the investigation. In summary, we find there is conclusive statistical and other evidence that median trees are associated with increased collisions, and increased collision severity. However, when considering only collisions located on the left side of the roadway, the linkages are weak. Nevertheless, there remains the expectation of increased collisions and greater severity of collisions in the presence of median trees. 1.4 Overview of the Rest of the Report The rest of this report contains four chapters and four appendices. Chapter 2 presents additional details concerning the development of the study data set used in the statistical analysis. Chapter 3 presents the detailed results from the statistical modeling work, including the presentation of simple accident rates and the specifications of the most statistically acceptable models relating collisions to highway characteristics. Chapter 4 presents the detailed findings of several additional investigations, including a review of selected original collision reports, an analysis of selected collision clusters, and comparisons of the suitability in modeling of posted speeds compared to measured speeds, and an assessment of differences in the TASAS and SWITRS data systems, conducted as a follow up to the Phase II report. Finally, Chapter 5 summarizes the principal conclusions and presents recommendations for additional investigations. The four appendices present summaries of the principal characteristics of the highway sections used in the analysis, as well as photos of these sections. 12 2. Development of the Phase III Data Set 2.1 Chapter Introduction This chapter describes the details of the data sets developed for the statistical analysis. It provides a full description of the sampling methodology, complete definitions of the variables used to represent highway characteristics, and information concerning the TASAS collision data that were used. 2.2 Sampling Considerations The data collection and modeling work previously conducted by this study, during Phase II, was based on a partial factorial design intended to ensure that enough field locations were included to provide an adequate amount of data to meet statistical accuracy targets. The accuracy targets were defined for accident rates stratified by the key physical features considered most likely to influence any relationship between collisions and median trees. This details of this factorial design are presented in the corresponding section of the Phase II report. 11 An analogous approach was taken to the data collection for Phase III, with a few changes motivated by experience from conducting the earlier parts of the study. The key variables used to guide the sampling of highway sections for the Phase III data collection are: Variations in posted speed, Variations in traffic volume ( ADT), Variations in median width, Variations in the setback from the median curb to median trees, Variations in assigned rate group. The last of these, rate groups, corresponds to the statewide categories by which California highway sections are grouped for the purpose of periodic reporting of accident rates and trends. A highway section is assigned to a particular rate group based on the type of highway, its surroundings, number of lanes, design speed, and in some cases the ADT. The basic goal of data collection is to ensure there are sufficient data collected for enough combinations of different levels of these key factors so the possible influence of these factors on collision frequency and severity can be determined. Note that, as in Phase II, posted speeds rather than measured speeds were used to guide the selection of study sections. This was for convenience since at the time the decisions regarding data collection were being made, data on measured speeds were not yet available. Actual measured speeds were used in the subsequent modeling and in the investigation reported in Section 4.4, which discusses the degree of correlation between posted speeds and actual speeds. Guided by the basic factorial design concepts discussed above and by the target level of exposure of 250 million vehicle miles, which is explained in detail in the Phase II report, our data collection effort was successful in adequately covering many of the factorial combinations that were targeted. Table 5 below shows the coverage of the data set with regard to three different categories of posted speeds and ADT. Table 6 shows the joint coverage of these two 11 Phase II Final Report. op cit. Section 2.3. 13 variables in combination. The cells show coverage of the data set measured in millions of vehicle miles ( MVM) of exposure. Table 5 shows that the data set has ample coverage for estimating the simple impacts on collisions of planting median trees, for different speeds and variations in ADT levels. The limited coverage for posted speeds of 50 mph and above is acceptable since these very high speed conventional highway sections are not of principal interest. The coverage for the lowest ADT category ( below 27,500 vehicles per day) is also limited, especially considering the absence of observations without median trees in that ADT range. However, we feel that the coverage in the medium to high ranges of ADTs is sufficient to examine the relationship between median trees and collisions across a sufficient range of ADT values. Table 5. MVM of Exposure by Posted Speeds, ADT, and Median Trees Median Type Median Type With Trees No Trees With Trees No Trees 30 35 1648 750 L 354 0 40 45 1424 1305 M 932 604 Posted Speed ( mph) 50+ 196 0 Average Daily Traffic H 1981 1451 Notes: 1. Low ADT is below 27,500, Medium is 27,500 to 40,000, and High is more than 40,000 vehicles per day in the year 2001. 2. MVM is section length times annual ADT times the number of days of accident data in each year, summed for highway sections with the stated characteristics and for the six years of coverage. 3. The target sample size is 250 MVM of exposure for each combination of characteristics. Table 6 shows that coverage is acceptable with regard to joint consideration of speeds and ADT. With the exception of sections with speeds 50 mph and above and in the low ADT category, there is ample coverage of other combinations of variables to estimate the main effects and their interactions. Clearly the effect of median trees can be determined with high statistical confidence for high ADT in both of the lower speed ranges and for median ADT in the 40 45 mph range. Table 6. MVM of Exposure by Posted Speeds Combined with ADT, and Median Trees Medians with Trees Medians without Trees Average Daily Traffic Average Daily Traffic L M H L M H 30 35 146 298 1204 0 0 750 40 45 126 521 777 0 604 702 Posted Speed ( mph) 50+ 82 114 0 0 0 0 Notes: 1. Low ADT is below 27,500, Medium is 27,500 to 40,000, and High is more than 40,000 vehicles per day in the year 2001. 2. The target sample size is 250 MVM of exposure for each combination of characteristics. 14 Similarly, Table 7 below shows the coverage of the data set with regard to different categories of median width and setback to median trees from the median curb. Table 8 shows the coverage of median width in combination with posted speeds. Table 9 shows the coverage for setback from the curb in combination with both posted speed and ADT. As before, each cell shows coverage measured in millions of vehicle miles ( MVM) of exposure for the given category. Table 7 shows that the data set provides good coverage for detecting the simple effect on collisions of having median trees across different median widths greater than 10 feet, and across different setback values with the exception of the very smallest (≤ 4 ft.). It is noteworthy that no state highways were found with median trees planted in medians less than 10 feet wide, even though many sections were found with setbacks to trees in the 4 6 foot range. Table 7. MVM of Exposure by Median Width and Setback to Median Trees Median Type Median Type With Trees No Trees With Trees No Trees 0 10 0 682 0 4 76 n/ a 10 16 2538 644 4 6 1679 n/ a Median Width ( feet) 16+ 729 728 6 8 1067 n/ a Setback: Curb to Med. Trees ( feet) 8+ 446 n/ a Note: 1. The target sample size is 250 MVM of exposure for each combination of characteristics. Table 8 shows that the data set permits many comparisons for medians 10 16 feet wide in both lower speed ranges, and for greater than 16 foot medians in the 40 45 mph range. As previously noted, comparing the effects of trees for 10 foot wide medians and less is not accommodated. Note that the coverage for 10 16 foot wide medians with trees in the 30 35 mph speed range is a little below the 250 MVM target threshold, but this is not a major deficiency. As before, we have a partial factorial design that provides opportunity to test relationships involving the major factors, as well as some second level interactions of interest. Table 8. MVM of Exposure by Median Width Combined with Speed, and Median Trees Medians with Trees Medians without Trees Posted Speed ( mph) Posted Speed ( mph) 30 35 40 45 50+ 30 35 40 45 50+ 0 10 0 0 0 532 150 0 10 16 1572 966 0 218 426 0 Median Width ( feet) 16+ 76 458 196 0 729 0 Note: 1. The target sample size is 250 MVM of exposure for each combination of characteristics. Table 9 shows a similar outcome with respect to coverage for testing the impacts on collisions of varying the setback between the median curb and median trees, for different posted speeds and ADT levels. Ample coverage exists for the 4 6 foot and 6 8 foot setback categories for both lower speed ranges, and also for the 8+ setbacks for the 40 45 mph range. Strong comparisons can also be made between the 4 6 foot and 6 8 foot setbacks for the high ADT range, between 15 the 6 8 foot and 8+ foot setbacks for the medium ADT range, as well as for variations in ADT within both the 4 6 foot and 6 8 foot setback categories. Table 9. MVM of Exposure by Speed and ADT Combined with Setback to Median Trees Medians with Trees Medians with Trees Posted Speed ( mph) Average Daily Traffic 30 35 40 45 50+ L M H 0 4 76 0 0 0 76 0 4 6 940 740 0 219 94 1367 6 8 632 352 82 135 317 615 Setback: Curb to Med. Trees ( feet) 8+ 0 332 114 0 446 0 Note: 1. The target sample size is 250 MVM of exposure for each combination of characteristics. Table 10 shows the breakdown with respect to coverage by rate group and median width. As previously noted, rate group is a code used by Caltrans to group highway sections for evaluating accident trends. The majority of sections in the data base are in rate groups H 38 and H 44, with two H 37s and just one H 43. The following table shows that coverage is sufficient to permit direct comparisons of the effects of median trees in the case of rate group H 38, for 10 16 foot medians, and for rate group H 44, for medians over 16 feet wide. In addition, we can compare collision experience between 10 16 foot and 16+ foot medians for both H 38 and H 44 highway sections, as well as between 0 10 foot and 16+ foot medians for H 44 highways. Table 10. MVM of Exposure by Rate Group Combined with Median Width, and Median Trees Medians with Trees Medians without Trees Median Width ( feet) Median Width ( feet) 0 10 10 16 16+ 0 10 10 16 16+ H 37 0 256 0 0 0 0 H 38 0 521 262 0 644 0 H 43 0 0 0 408 0 0 Rate Group H 44 0 1762 467 274 0 729 Note: 1. The target sample size is 250 MVM of exposure for each combination of characteristics. Finally, Table 11 below shows a similar breakdown including rate group and ADT category. Direct comparisons of the impacts of median trees on collision experience can be made for the H38 and H 44 rate groups, for both medium and high ADT ranges. ( Although coverage for the H 44 rate group in the medium ADT range is somewhat below the target, that will not seriously harm the comparison.) Similarly, the impact on collision experience for medians with and without trees can be compared between the medium and high ADT levels, for both the H 38 and H 44 highway types. 16 Table 11. MVM of Exposure by Rate Group Combined with ADT Category, and Median Trees Medians with Trees Medians without Trees Average Daily Traffic Average Daily Traffic L M H L M H H 37 146 110 0 0 0 0 H 38 73 395 315 0 426 218 H 43 0 0 0 0 0 408 Rate Group H 44 135 427 1667 0 177 825 Notes: 1. Low ADT is below 27,500, Medium is 27,500 to 40,000, and High is more than 40,000 vehicles per day in the year 2001. 2. The target sample size is 250 MVM of exposure for each combination of characteristics. To summarize, the above tables show that the twenty nine highway sections contained in the Phase III data set provide adequate coverage across many variations in the key variables. Initially, we were concerned that limiting the data collection to only state highways would make it difficult if not impossible to find a sufficient number of sections with median trees and combinations of narrow medians, narrow setbacks, and high speeds inconsistent with the side clearance standard found in the Caltrans Highway Design Manual. This turned out not to be as much of a problem as anticipated. Based on the information presented in this section, we believe the Phase III data set provides adequate coverage to support multivariate statistical modeling in order to explore the consequences of variations in these key variables. 2.3 Coding of Highway Section Characteristics The highway section characteristics used in Phase III of the study are mostly the same as were used in Phase II. The principal additions in Phase III are several parameters for measured speeds, and section rate group codes. The values for most characteristics were obtained through field measurements and from various published sources. The following is a detailed list of the section characteristics in the data set, providing details on coding methods and sources of information. Table 12. Coding of Highway Section Characteristics Characteristic Coding Method and Source of the Data Item Median Type Field Observation – Curbed w/ trees or Curbed – no trees Beginning & Ending Postmiles From CA Highway Log – A scale ( miles) for locating state highway features. The difference is the section length, if no postmile discontinuity occurs in the section. Posted Speed Field observation – Categorized as 30 35, 40 45, and 50+ mph. No sections have posted speeds under 30 mph. 50+ mph sections were excluded from most analyses. Average Speed From district speed studies, where available ( mph) – The average of any measured speeds in the section ( during or close to the 1996 2001 analysis period). 17 Characteristic Coding Method and Source of the Data Item 85% ile Speed From district speed studies – The average value below which 85% of the measured vehicle speeds fall ( also called “ critical speed”) Top of Pace Speed From district speed studies – The average top of the 10 mph speed range in which most measured speeds fall. % in Pace Range From district speed studies – The average % of measured speeds in the most observed 10 mph speed range. ( This estimates the variability of section speeds.) Bottom & Top of Pace % Range From district speed studies – The smallest and largest of the % in Pace Range values observed for the section. Section Length Calculated from postmile values ( in miles) Number of Lanes Field observation – The single direction lane count. Average Daily Traffic From: http:// www. dot. ca. gov/ hq/ traffops/ saferesr/ trafdata  Section values were interpolated/ extrapolated from the posted data for each year. Categorized as L (≤ 27,500), M ( 27,501 40,000), H(> 40,000) based on the year 2001. Total Median Width Field measurement – Curb to curb values. Categorized as 0 10, 10.1 16, 16.1+ feet. Median Shoulder Width Field measurement ( feet) – Stripe to curb. If no stripe, is estimated as total median lane width minus 12 feet. Distance – Curb to Median Trees Field measurement ( feet) – Categorized as 0 4, 4.1 6, 6.1 8, 8.1+ feet. Lane # 1 to Median Trees Sum of the previous two measurements – Categorized as 0 4, 4.1 6, 6.1 8, 8.1+ feet. Setback to Right Side Trees Field measurement ( feet) – Typical curb to tree distance. Median Curb Height Field measurement ( inches). Right Shoulder Width Field measurement ( feet) – Stripe to curb. If no stripe, is estimated as total right lane width minus 12 feet. Tree Trunk Diameter Field measurement – Typical median tree measured 4 feet above the ground ( feet). Right Side Curb Height Field measurement ( inches). Lane Widths (# 1 and RS Lanes) Field measurement ( feet) – Assumed 12 feet if no stripe. Million Vehicle Miles ( MVM) Calculated from section length and ADTs – Total estimated exposure for the six year ( 1996 2001) period. Nearby Land Use Field observation – Categorized as high, medium or low density commercial; high, medium or low density other Cross Street Density Field observation – Categorized as Low, Medium, or High density ( compared to other sections). 18 Characteristic Coding Method and Source of the Data Item Right Side Parking? Field observation – Categorized as Yes or No Right Side Trees? Field observation – Categorized as Yes or No Right Side Sidewalks? Field observation – Categorized as Yes or No Median Trees Aligned? Field observation – Categorized as Yes or No Highway Curvature Field observation – Categorized as L ( predominately straight), M ( gently curving), H ( tight curves), 90o turns Highway Grades Field observation – Categorized as L ( predominately level), M ( rolling, gentle grades), H ( steep grades) Ride Side Utility Poles Field observation – Categorized as Yes far from curb, Yes close to curb, or No Rate Group Determined from observed data, information in the California Highway Log, and design speed data from the Caltrans TASAS Unit, using definitions from the report 2001 Collision Data on California Highways. Expected Accident Rates ( Total and F& I) Average statewide accident rates for the rate group, obtained from 2001 Collision Data on California Highways The full data set used in the study is on line at http:// ceenve. calpoly. edu/ sullivan/ trees/. 2.4 Coding of Collision Data As previously mentioned, Phase II of this study used a data set containing a mix of state highway sections and sections under local jurisdiction. This was done in order to ensure having enough data with which to perform the statistical modeling. As a result, the data set for Phase II contained collision data from two sources: the California Highway Patrol ( CHP) maintained SWITRS data system for the local facilities, and the Caltrans maintained TASAS data system for the state highways. Concerns about possible incompatibilities between the two major state collision data systems led us to limit the Phase III investigation to state highway sections only. ( The experience of Phase II suggested it would be possible, after all, to find enough state highway sections to perform the statistical modeling, without having to fall back on local facilities to obtain enough pertinent observations.) The issue of incompatibilities between SWITRS and TASAS and how these might have affected the Phase II results is addressed in Section 4.5 of this report. In Phase III of the study, only state highway collision data from the TASAS system were used. Table 4 lists the data items extracted from TASAS for each highway section and included in the study data set. As noted, these data can be seen in their entirety in the study data set that is on line at http:// ceenve. calpoly. edu/ sullivan/ trees/. The overall data set contains a total of 228 different data items describing the number and characteristics of the collisions that occurred on each highway section. Unique column names were assigned to keep the information organized. Even so, the number of collision variables in combination with the 52 variables describing other section characteristics exceeded the 256 column capacity of Excel to store this information. For this reason, and for the sake of good organization, the Phase III data set consists of six Excel data files. They are: 19 1. The basic section characteristics ( see Section 2.3) combined with data for all the collisions occurring in each section during the 1996 2001 study period, regardless of location; 12 2. The basic section characteristics combined with collision data, omitting any collisions that occurred exclusively in the right lane, the right shoulder or beyond ( i. e., for which median characteristics can be assumed irrelevant); 3. The basic section characteristics combined with data for any collisions that involved the left ( median) shoulder, the median itself, or beyond ( i. e., for which median characteristics appear most relevant). 4. The same as data set # 1, except collisions within intersections are omitted. 5. The same as data set # 2, except collisions within intersections are omitted. 6. The same as data set # 3, except collisions within intersections are omitted. The first data set is called the “ Total Collisions – TC” file, the second the “ No Right Side – NRS” collisions file, the third the “ Left Side Only – LSO” collisions file, the fourth the “ Total Collisions No Intersctions – TCNI” file, the fifth the “ No Right Side No Intersections – NRSNI” file, and the sixth the “ Left Side Only No Intersections – LSONI” file. The collisions in each file are generally a subset of the file immediately above. Most of the Phase III modeling work utilized the second, third, fifth and sixth files, whereas the Phase II modeling work used a file similar to the first, although mainly including different highway sections. The highway section characteristics are duplicated in all files in order to faciltate working with each group of collisions independently. The processing to assign collisions to the various files examined fiveTASAS data fields – the “ Primary Location of Collision” field, three “ Other Location of Collision” fields, and the “ Intersection/ Ramp Location” field. The first four fields are coded separately for each party involved in the collision. For example, if a collision involved three vehicles, a total of twelve location fields were examined. Among the possible codes in these location fields, six were of principal interest: A – Beyond median or stripe ( left) B – Beyond shoulder driver’s left C – Left shoulder area F – Right lane G – Right shoulder area H – Beyond shoulder driver’s right If all the location fields for a collision contain only codes F, G, or H ( nothing else), that collision was excluded from the “ No Right Side” collision data sets; all other collisions being included. If any of the location fields for a collision contain A, B, or C, that collision was included in the “ Left Side Only” data sets; regardless of what other locations might also be coded. The following Intersection/ Ramp Location ( IRL) codes were of principal interest: 5 – Collision located within an intersection 6 – Collision located outside intersection, non state route 12 Collisions on intersecting cross streets, which also appear in TASAS, were omitted from all data sets. 20 Collisions with IRL = 6 were omitted from all six data sets while collisions with IRL = 5 were omitted from data sets 4 through 6. As noted, each file contains a very large number of collision counts, characterizing all the collisions in the group and just the collision involving fatalities and injuries ( F& I). Counts are further stratified by numerous collision characteristics, which are listed previously in Table 4. 21 3. Results from Modeling Based on TASAS Collision Data 3.1 Chapter Introduction This chapter presents the details of the statistical modeling. As described in Section 1.2, the modeling used three separate approaches: ( 1) testing several forms of generalized linear models, ( 2) estimating simple accident rates and confidence intervals, and ( 3) chi square testing of differences in collision characteristics. In all cases, the goal was to try to detect statistically significant differences in the collision estimates for highway sections with and without median trees. The possible effects of median trees were compared for many variations in the other highway characteristics listed in Table 2. The detailed findings are presented in the three sections that follow. The overall conclusion is that elusive but statistically significant associations exist between collision frequency and collision severity and the presence of median trees. However, these associations are weak when the frequency of Left Side Only collisions is considered. Collision frequency and severity are usually ( but not always) less for lower actual ( but not posted) speeds but, surprisingly, lower collision frequency and severity are associated with narrower medians. However, accident rate estimates indicate that differences in collision rates with and without median trees are largest for the lowest category of 85% ile speed considered. 3.2 Generalized Linear Modeling As described in Section 1.2, three different generalized linear model structures were tested with a large variety of candidate explanatory variables. Model GL 1: iXXMEDTREEADTLiERRCOLLiiiii)(... 25143210++++++= ββββββε ( this error term ERRi is assumed to follow the negative binomial distribution) Model GL 2: iXXMEDTREEiiiERRADTLCOLLiii)(... 231210++++= ββββε ( this error term ERRi is assumed to follow the Poisson distribution) Model GL 3: iXXMEDTREEALLiIFiERRCOLLCOLLiii)()(... & 231210++++= ββββε ( this error term ERRi is assumed to follow the Poisson distribution) Where: COLLi is the observed annual number of collisions on section i – in some models this is the annual collision count for a particular year, in others it is the six year average; Li is the section length ( miles); ADTi is the section average daily traffic; MEDTREEi is either 0 or 1, indicating whether section i has median trees; ε is the base of the natural logarithms (≈ 2.718); Xi1, Xi2, etc. are other section characteristics from Table 2; β0, β1, β2, etc. are parameters obtained from fitting the model to the data; 23 ERRi is an error term accounting for random effects not explicitly considered in the model. For each model tested, the statistical significance of the MEDTREEi variable was scrutinized to see if, in the presence of other variables, median trees appear to be significantly associated with the number of collisions ( in GL 1 and GL 2) or with the severity ratio ( in GL 3). Models GL 1 and GL 2 were tested for all collisions and for fatal and injury ( F& I) collisions alone, the latter being another indication of collision severity. As noted in Section 1.2, Model GL 1 is regarded as conceptually superior to Model GL 2 for representing collision frequency since it incorporates the section length and ADT variables in a more general manner. In an initial round of model testing, with intersection collisions included, each highway characteristic was examined by itself in addition to only the variables required in each basic model structure. The purpose of this was exploratory, to see under what circumstances, if any, the Medtree variable appeared to be statistically significant. In each case, the statistical significance of each included variable was given by its P value. If the P value for a given variable falls in the range 0 – 0.05, this indicates that the variable’s contribution to variations in the dependent variable ( the number of collisions or the severity ratio) is statistically significant at the 95% confidence level or better. If the P value is greater than 0.05, this indicates less confidence. For example, if P= 0.40, the corresponding variable would be judged significant at the 60% confidence level, which is quite insignificant. The tables below present most of the results of these initial model tests. Table 13 and Table 14 show results for models run using the “ No Right Side Collisions” data set, the first including all such collisions, the second including F& I collisions only. As noted, intersection collisions are included in all cases. Table 15 and Table 16 show the models run using the “ Left Side Only Collisions” data set. ( See Section 2.4 for the precise definitions of these two data sets.) In each case, the table shows, for each model type, the variables included and their corresponding P values, which indicate their statistical significance. 13 Cases where all variables are or are close to significant at the 95% level are highlighted. Models for which values are shown in bold and italics have all significant parameters and are discussed in further detail below. For convenience, in the GL 1 models, P values are omitted for the variable Li ( section length) because section length is always highly significant, usually with P values less than 0.0001. The models in the following tables generally are based on data for 23 of the 29 highway sections, omitting sections with 30 mph or 50 mph posted speeds, and in the H 37 or H 43 rate groups. This was done because sections with these characteristics either all have median trees 13 In an hypothesis test to test if a relationship exists ( such as between median trees and collisions), we assume that there is no relationship and then use our sample data to try to refute this assumption. Such tests are commonly conducted at the 5% level of significance, or, in the terminology of some researchers, the 95% level of confidence. In the tests conducted in this study, the P values for various tests are reported. Each P value is the probability of obtaining a value of our test statistic less likely than our observed value assuming no relationship between our response variable ( number of accidents, etc.) and the predictors ( medtree, posted speed, median width, etc.) If a P value is less than 0.05 ( 5%), the assumption of no relationship is viewed as very unlikely, and we conclude that a relationship between the variables exists at the 5% significance level ( the 95% confidence level). Essentially this says that the result we obtained would happen less than once out of 20 times if there was no relationship, so there is at most a 5% chance of making a mistake by concluding there is a relationship. When the test yields a P value greater than 0.05, the result tells us how far we would have to “ lower the bar” to conclude that the relationship exists. For example, if the P value were 0.15, one would have a 15% chance of making a mistake by concluding there is a relationship. In other words, the higher the P – value, the less evidence that there is a relationship, and the more evidence that there is no relationship. 24 or all do not have trees, therefore the effects of the median trees can not be discerned. ( Note that some test models were fit to the data for all 29 sections, with generally similar results.) Table 13. Significance of Initial Models for All “ No Right Side” Collisions Model GL 1 Model GL 2 Model Variable P Value ADTi P Value14 P Value 1 Medtree 0.104 0.003 0.013 2 Medtree 0.16 0.008 0.02 Posted Speed 0.35 0.89 2a Medtree 0.27 0.004 0.09 85% ile Speed 0.73 0.94 3 Medtree 0.15 0.0007 0.07 # 1 Lane Width 0.089 0.117 4 Medtree 0.11 0.0046 0.19 Rate Group 0.98 0.85 5 Medtree 0.268 0.01 0.02 MedWidthCat 0.577 0.84 6 Medtree 0.097 0.004 0.017 # lanes ( quan.) 0.63 0.53 7 Medtree 0.091 0.002 0.017 Curbheight 0.027 0.53 8 Medtree 0.057 0.003 0.024 X Street Density 0.169 0.95 9 Medtree 0.105 0.004 0.024 RS Parking 0.97 0.94 10 Medtree 0.067 0.0006 0.017 RS Sidewalks 0.036 0.324 11 Medtree 0.108 0.006 0.014 Curvature 0.84 0.72 12 Medtree 0.079 0.003 0.01 Grade 0.124 0.27 14 Since ADTi is in all GL 1 models, its P value appears in a separate column to make the table more compact. Li, which also is in all GL 1 models, has P values always less than 0.0001 and is not shown. 25 Model GL 1 Model GL 2 Model Variable P Value ADTi P Value14 P Value 13 Medtree 0.001 0.0006 0.005 LandUseCat15 0.0035 0.397 It should be noted that in the case of the GL 2 models a correction for over dispersion was necessary in order to obtain suitable estimates of the standard errors. Over dispersion in the uncorrected data presents a problem when the variance is much larger than the mean. The correction results in models that are consistent with their underlying assumptions, and leads to meaningful measures of significance ( P values). Patterns of residuals were also examined for the different model forms and judged to be consistent with the a priori assumptions about the error term distributions ( either negative binomial or Poisson, depending on the model). As seen above and in other tables below, very few of these simple models have statistically significant parameter values, that is, where all P values are less than 0.05. In Table 13, the presence of median trees is significant only for Model GL 2, where entered alone, and for Model GL 1 where entered with land use type. Model GL 1 was very close to significant if the presence of sidewalks is included, which also reflects the nature of the surrounding development. When only fatal and injury collisions are considered, the only simple relationship showing statistically significant parameters ( in Table 14) is Model GL 2, when the median width category is also included, and Model GL 1, when land use type is also included. When only the presence of median trees is included, both the GL 1 and GL 2 models are close to significant ( P values about .06). Medtree is not significant in any of the GL 3 models, in fact in most of these models the parameter estimates for Medtree= 0 are positive, implying greater severity where median trees are not present. Table 14. Significance of Initial Models for F& I “ No Right Side” Collisions Model GL 1 Model GL 2 Model GL 3 Model Variable P Value ADTi P Value P Value P Value 1 Medtree 0.068 0.0005 0.06 0.68 2 Medtree 0.16 0.008 0.072 0.73 Posted Speed 0.35 0.96 0.82 2a Medtree 0.25 0.002 0.08 0.53 85% ile Speed 0.46 0.56 0.20 3 Medtree 0.09 0.0001 0.20 0.73 # 1 Lane Width 0.038 0.19 0.95 4 Medtree 0.07 0.001 0.08 0.65 Rate Group 0.97 0.68 0.76 15 The model with land use is based on 22 highway sections rather than 23, since only one section with trees has the “ high commercial” land use, therefore no comparison for the effect of trees on collisions is possible for that land use category. 26 Model GL 1 Model GL 2 Model GL 3 Model Variable P Value ADTi P Value P Value P Value 5 Medtree 0.037 0.002 0.004 0.31 MedWidthCat 0.37 0.038 0.03 6 Medtree 0.05 0.002 0.11 0.77 # lanes ( categ.) 0.76 0.93 0.49 7 Medtree 0.063 0.0006 0.05 0.74 Curbheight 0.48 0.26 0.017 8 Medtree 0.027 0.0003 0.055 0.88 X Street Density 0.10 0.74 0.76 9 Medtree 0.068 0.001 0.06 0.86 RS Parking 0.80 0.67 0.53 10 Medtree 0.065 0.0003 0.06 0.79 RS Sidewalks 0.365 0.74 0.095 11 Medtree 0.098 0.0001 0.056 0.72 Curvature 0.47 0.57 0.75 12 Medtree 0.065 0.0006 0.073 0.52 Grade 0.71 0.74 0.096 13 Medtree 0.001 0.0001 0.0073 0.48 LandUseCat 0.006 0.273 0.31 Using the reduced LSO data set containing only the collisions that intrude into the median shoulder, the median, or beyond ( Table 15 and Table 16), the presence of median trees is shown to be mostly not significant. The exception is one of the F& I models in Table 16 where the combination of median trees and median width for Model GL 2 yields statistically significant parameters. Note that two sections without median trees have median width < 10 feet but there are no corresponding medians with trees in this category. If these two sections are excluded, the parameters of the GL 2 model become not significant ( P= 0.067 and 0.25 for Medtree and MedWidthCat, respectively). As before, the Medtree variable is consistently not significant ( by a wide margin) in the GL 3 severity models. Overall, it appears in these simple models with the Left Side Only data set that the influence of median trees is generally not significant. It should be noted, however, that with this data set the model fitting procedure was often unable to converge within the usual bounds; therefore results are ( at best) approximate. These P value estimates are based on approximate normal distributions of maximum likelihood estimators. 27 Table 15. Significance of Initial Models for All “ Left Side Only” Collisions Model GL 1 Model GL 2 Model Variable P Value ADTi P Value P Value 1 Medtree 0.38 0.019 0.094 2 Medtree 0.44 0.04 0.089 Posted Speed 0.58 0.66 2a Medtree 0.46 0.014 0.087 85% ile Speed 0.47 0.36 3 Medtree 0.47 0.005 0.33 # 1 Lane Width 0.13 0.087 4 Medtree 0.47 0.04 0.12 Rate Group 0.53 0.77 5 Medtree 0.55 0.075 0.07 MedWidthCat 0.57 0.49 6 Medtree 0.51 0.02 0.59 # lanes ( categ). 0.79 0.35 7 Medtree 0.38 0.02 0.10 Curbheight 0.94 0.99 8 Medtree 0.29 0.02 0.19 X Street Density 0.47 0.87 9 Medtree 0.39 0.039 0.08 RS Parking 0.57 0.59 10 Medtree 0.34 0.005 0.116 RS Sidewalks 0.034 0.365 11 Medtree 0.37 0.01 0.135 Curvature 0.29 0.182 12 Medtree 0.29 0.02 0.066 Grade 0.056 0.20 13 Medtree 0.11 0.018 0.06 LandUseCat 0.26 0.86 28 Table 16. Significance of Initial Models for F& I “ Left Side Only” Collisions Model GL 1 Model GL 2 Model GL 3 Model Variable P Value ADTi P Value P Value P Value 1 Medtree 0.87 0.03 0.44 0.27 2 Medtree 0.81 0.028 0.35 0.31 Posted Speed 0.67 0.43 0.48 2a Medtree 0.84 0.03 0.11 85% ile Speed 0.77 0.78 3 Medtree 0.99 0.009 0.98 0.40 # 1 Lane Width 0.10 0.05 0.38 4 Medtree 0.97 0.07 0.49 0.27 Rate Group 0.56 0.74 0.83 5 Medtree 0.53 0.06 0.06 0.97 MedWidthCat 0.25 0.05 0.06 6 Medtree 0.88 0.07 0.47 0.30 # lanes ( quant.) 0.96 0.76 0.58 7 Medtree 0.76 0.028 0.34 0.16 Curbheight 0.076 0.085 0.002 8 Medtree 0.68 0.05 0.49 0.47 X Street Density 0.45 0.85 0.89 9 Medtree 0.87 0.156 0.28 0.40 RS Parking 0.17 0.30 0.38 10 Medtree 0.85 0.02 0.44 0.36 RS Sidewalks 0.45 0.87 0.12 11 Medtree 0.88 0.026 0.51 0.33 Curvature 0.49 0.48 0.51 12 Medtree 0.86 0.036 0.45 0.14 Grade 0.56 0.94 0.08 13 Medtree 0.31 0.019 0.17 0.17 LandUseCat 0.13 0.94 0.28 This initial exploratory modeling produced mixed results. There is no consistent evidence that the presence of median trees is systematically associated with more collisions or greater collision severity. On the other hand, especially using the larger data set ( which excludes only the right side collisions), some significant associations are evident. When the data set is limited to left side collisions, there appears no strong statistical evidence that the number or the severity of collisions are associated with the presence of median trees. 29 On the other hand, in these simple model forms, the effects of median trees may be hidden by associations between collisions and combinations of other section characteristics that need to be controlled for in order for the effects of median trees to become visible. This can be especially true if the association between collisions and median trees is weak compared to the influence of the other variables. For this reason, in depth multivariate modeling was performed. Based on logic and insights gained from the preceding analysis of simple model forms, a “ short list” of candidate predictor variables was postulated. This showed some of the candidate variables having little statistical association with collisions. A pruning procedure was then followed through which the least significant predictors, except for Medtree, were eliminated. The pruning continued until all of the variables remaining in the model were significant, or almost so. The final set of candidate predictor variables for the multivariate models is the following: Medtree – Median Trees Present ( Yes, No) Speed ( both posted speed – 35, 40, 45 – and 85% ile speed – 40, 45, 50 – were tested) Median Lane Width (# 1 Lane) Rate Group ( H 38 or H 44) Median Width Category ( 10 16 or > 16 ) Median Curb Height Number of Lanes ( either 2, 3, 4, or 2, 3& 4, coded as a categorical variable) Cross Street Density ( L, M, H) Right Side Sidewalks ( Yes, No) Land Use Type ( Commercial, Other) As previously noted, the amount of variation in some variables was limited by the data set. For example, all 30 mph speed sections had median trees, therefore these 30 mph sections were not included due to the lack of directly comparable sections without median trees. The three model forms ( GL 1, GL 2, GL 3) were tested for four data sets ( NRS – “ No Right Side,” LSO – “ Left Side Only,” NRSNI – “ No Right Side No Intersections,” and LSONI – “ Left Side Only No Intersections”) and the GL 1 and GL 2 forms were tested for all collisions and for F& I collisions separately. Most of these tests produced models with some parameters, often including the Medtree parameter, not statistically significant. Selected results of the multivariate model tests are summarized in Table 17 and Table 18 below. Although most models that fit the data poorly are not shown, a number are shown below for comparison with models with similar specifications that fit the data well. Models in which all the parameters are statistically significant ( or close) are highlighted in bold italics. Most of these are subsequently discussed in detail. In cases of parameter values “ close” to significant, two levels are identified – parameters significant at the 90 95% confidence level are coded “ C1,” while parameters significant at the 80 90% level are coded “ C2.” In comparing the models in Table 17 and Table 18, a few noteworthy patterns are evident. First, it is clear that the three basic model forms usually give very different results for the same combination of variables. That GL 3 performs very differently from GL 1 and GL 2 is expected, since GL 3 models severity, while the others model collision frequency, although in different ways. GL 1 is conceptually superior to GL 2 since it provides more flexibility in modeling the influence on collisions of different section lengths and ADTs. Although different, the GL 1 and GL 2 models for a given specification often show quite a bit of similarity in their outcomes. 30 Usually, the models fit to the data sets that exclude intersection collisions are similar to the models that include these collisions. However, their statistical properties are somewhat stronger. On the other hand, achieving model convergence proved more difficult for the smaller non intersection collision data sets, especially for the smallest LSONI data set. Another noteworthy factor is that substituting 85% ile speed for posted speed, all other factors being equal, generally produces different results. However, in some cases, these differences are small. This indicates that even though posted speeds and actual measured speeds are highly correlated ( see Section 4.4), they are not equivalent for statistical modeling. ( As discussed in Section 4.4, both speed measurements have certain practical limitations, so it is difficult to know whether one is better than the other. Consequently, we considered both. A final observation about these alternative multivariate models is the degree of volatility observed in fitting the models to the different data sets. Adding or eliminating one variable typically caused large changes in parameter values, and corresponding levels of significance. In part, this volatility is due to the relatively small data sets used, even though nearly all suitable and comparable highway sections in the State of California were included. In part, the volatility may be due to the diversity and random nature of the collisions themselves. Also, collision causes are complex and varied, and simple general explanations simply are not possible. The “ best” of the models identified in Table 17 and Table 18 are discussed in detail below. Table 17. Summary of Multivariate Models with Intersection Collisions Included Significance of Included Optional Variables ( See Note Below) Model Form ( GL?) Dataset Used Collisions Included Posted Speed 85% ile Speed Median Width # 1 Lane Width Median Curb Ht. Land Use Sidewalks X St. Density No. of Lanes Rate Group All Pars. Significant? Medtree P Value 1 NRS All C2 S C .02 1 NRS All N C1 S N N N .03 1 NRS All C2 S S C2 N N .02 1 NRS F& I C2 C1 C1 C1 C .002 1 NRS F& I C2 S C1 C .01 1 NRS F& I C1 S S C .07 1 NRS F& I C2 S N S N N N .14 1 NRS F& I N S C2 S C2 C2 N .13 1 NRS F& I S N S S C1 N .01 1 NRS F& I S N C1 S S N .07 1 LSO All S S S N N Q .44 1 LSO All N N N N .66 1 LSO F& I N N C2 N .04 2 NRS All S S S S S Y .01 2 NRS All N S C1 N N N .06 31 Significance of Included Optional Variables ( See Note Below) Model Form ( GL?) Dataset Used Collisions Included Posted Speed 85% ile Speed Median Width # 1 Lane Width Median Curb Ht. Land Use Sidewalks X St. Density No. of Lanes Rate Group All Pars. Significant? Medtree P Value 2 NRS All C2 N N .05 2 NRS F& I S S S S S S Y .01 2 NRS F& I N S C2 C1 N N N .19 2 NRS F& I C2 C1 C1 C1 N N .02 2 NRS F& I S N N N N .01 2 NRS F& I N N N N N N .10 2 NRS F& I C1 N N N .02 2 NRS F& I N C1 C2 N .24 2 LSO All S S S S C .12 2 LSO All N N N N .49 2 LSO F& I N C2 N N .08 3 NRS  C1 N N N N N .25 3 NRS  N N N N N N .66 3 NRS  C2 N N N N N N .. 31 3 NRS  N N C2 N N N N .76 3 NRS  N S N N N N .11 3 NRS  S N N C2 N .15 3 NRS  N N N .78 3 NRS  S N C2 N .14 3 NRS  N N N N .58 3 LSO  C1 S S C .02 3 LSO  N S N .31 3 LSO  S C1 C .12 3 LSO  C2 S N S N .04 3 LSO  N C1 N N N Q .89 Notes: 1. The statistical significance of each model parameter is coded as follows: S – Parameter is significant at the 95% confidence level, C1 – Parameter is significant at the 90 95% confidence level, C2 – Parameter is significant at the 80 90% confidence level, N – Parameter is not significant ( i. e., significance is less than the 80% level). 32 2. The next to last column showing the significance of all model parameters is coded as: Y – All model parameters are significant at the 95% level, C – All model parameters are acceptable ( all coded S, C1 or C2), N – At least one model parameter is not statistically significant, N Q – Parameters are not significant and the model did not converge normally. Table 18. Summary of Multivariate Models with Intersection Collisions Excluded Significance of Included Optional Variables ( See Note Below) Model Form ( GL?) Dataset Used Collisions Included Posted Speed 85% ile Speed Median Width # 1 Lane Width Median Curb Ht. Land Use Sidewalks Average ADT No. of Lanes Rate Group All Pars. Significant? Medtree P Value 1 NRSNI All S S S S S Y .02 1 NRSNI All C2 S S S S C .01 1 NRSNI All C2 S S S S C .02 1 NRSNI All C1 S S S C .03 1 NRSNI All N S S S S C1 N .004 3 NRSNI  S S C2 C1 C .06 3 NRSNI  S S C1 S C .03 3 NRSNI  S C1 N N .28 3 NRSNI  S C2 N .49 3 NRSNI  S S N N S N .13 3 NRSNI  S S C1 N .22 3 LSONI  S Y .04 3 LSONI  C1 S N N .31 3 LSONI  C2 S N .44 3 LSONI  S C2 N N .65 3 LSONI  S C1 N .40 3 LSONI  S N .72 See notes for Table 17. The following provides further detail and discussion about selected multivariate models for which all parameters are statistically significant at the 95% level ( or close). The Best Models of Type GL 1 Only one of the GL 1 models tested has parameters that are all significant at the 95% level, but seven other models came close. All were developed using the No Right Side collisions data sets. These models are highlighted in the tables above. None of the GL 1 models developed 33 using the Left Side Only data sets gave acceptable statistical properties. Of all the candidate variables tested, the # 1 ( median) lane width and the surrounding land use were most often linked with the number of collisions. Median curb height appears in four models, a speed variable appears in three, and median width appears in two of the models. The first and simplest GL 1 model appears below in Table 19. It was estimated using the data set containing all of the No Right Side collisions and includes intersection collisions.. Table 19. Multivariate Model GL 1 A Estimated for NRS ALL Collisions Data Points ( N): 23 Degrees of Freedom ( DF): 17 Variable Estimate Standard Error P Value Intercept . 0965 1.3595  Section Length 0.3578 0.0415 < 0.0001 Average ADT 0.2694 0.0691 0.0005 Medtree = 0  0.3393 0.1430 0.024 Median Lane Width 0.1695 0.1032 0.109 Land Use = Commercial 0.3959 0.1373 0.008 The following statistics appear in the table: The degrees of freedom ( DF) are the number of data points ( 22) minus the number of estimated parameters ( 10). The Standard Error measures the amount of variation in each parameter estimate. The P value measures the statistical significance of each parameter’s contribution to the model, with smaller being better. Values under 0.05 indicate significance at the 95% confidence level. Many variables in these models are categorical, where one category is selected as the base. For example, in the above model, the base categories for the categorical variables are Medtree= 1 and LandUse= Other. ( SectionLength, AverageADT, and MedianLaneWidth are continuous variables.) Each categorical parameter estimate shows the effect of the indicated category relative to the base. For example, in the above model, the effect on collisions of Medtree= 0 ( no median trees) is negative ( i. e., fewer collisions are expected) while the effect on collisions of commercial land use is positive ( i. e., more collisions are expected than for other land uses). Therefore, the model suggests that highway sections with median trees are expected to have more collisions than sections without trees, when the effects of section length, ADT, median lane width, and surrounding land use are controlled for. The model also suggests that the number of collisions increases with ADT but much less than proportionally. Specifically, in this version of Model GL 1: iADTiCOLL0.2694ε≈ Thus, the model implies that if ADT doubles and everything else remains the same, the number of collisions would increase by a factor of 2694.0) 2694.0)( 2(/ εε or 1.3. This is not unreasonable. On the other hand, if the section length doubles, with everything else the same, collisions would 34 increase by a factor of 1.43. On face, this may not seem reasonable. 16 In general, one would not want to use a model of this type for accident prediction. However, the model does show that there is a statistically significant association between median trees and the total number of NRS collisions. It also suggests that the number of collisions is positively associated with increasing median lane width. ( This relationship is also observed in the simple accident rate models presented later in Section 3.3.) Note however that the median lane width variable is not quite significant at the 95% level. The one model that was found in which all parameters are significant at the 95% level was estimated using the data for all No Right Side collisions, with collisions at intersections excluded. This model appears in Table 20 below. Table 20. Multivariate Model GL 1 B Estimated for NRSNI ALL Collisions Data Points ( N): 22 Degrees of Freedom ( DF): 14 Variable Estimate Standard Error P Value Intercept  2.2582 1.1445  Section Length 0.3532 0.0321 < 0.0001 Average ADT 0.3479 0.0622 < 0.0001 Medtree = 0  0.2983 0.1192 0.019 # Lanes = 2 0.2760 0.1200 0.035 Median Curb Height 0.0716 0.0265 0.011 Median Lane Width 0.2453 0.0831 0.009 Land Use = Commercial 0.3940 0.1119 0.003 On the whole, there is considerable consistency in the parameters that are common to the above two models. This new model implies that sections without median trees in our sample have times the total non intersection collisions compared to sections with median trees, when differences due to section length, ADT, number of lanes, # 1 lane width, curb height, and land use are separately accounted for. Note that the number of lanes enters as a category variable, with directional two lane sections associated with more collisions than the alternative base case, which is three or four directional lanes. Median curb height enters this model with a positive parameter value, meaning that, in this data set, higher median curbs are associated with more collisions, everything else being equal. 74.02983.0=− ε In neither of these initial models did variables measuring median widths or speeds enter as being even close to statistically significant. In fact, median width was never found significant in 16 A peer reviewer comments that it may “ not seem reasonable if you think that twice the length should be twice the accidents. However, section length in the database is often determined by the distance between major intersections ( where ADT may change). Therefore, section length is associated with intersection density and other variables. For this reason ( when access, either by intersections or by driveways and commercial access is not accounted for) L is a proxy for all these variables. Because more than half of all accidents are intersection and access related, not having these variables in the model will generally produce strange results. In particular, you will not know whether what you attribute to median trees really reflects an association between these and access density.” 35 any of the GL 1 models based on all No Right Side collisions. However, median width did enter into two models fit to No Right Side fatal and injury ( F& I) collisions, as seen later in this section. Two models based on all No Right Side collisions, excluding intersections, were found to have speed variables close to statistically significant. These appear below in Table 21 and Table 22. Table 21. Multivariate Model GL 1 C Estimated for NRSNI ALL Collisions Data Points ( N): 22 Degrees of Freedom ( DF): 13 Variable Estimate Standard Error P Value Intercept  2.1026 1.2187  Section Length 0.3598 0.0384 < 0.0001 Average ADT 0.3010 0.0644 < 0.0001 Medtree = 0  0.3950 0.1458 0.009 85% ile Speed = 40  0.3984 0.1931 0.124 85% ile Speed = 45  0.1617 0.1522 0.124 Median Curb Height 0.0675 0.0283 0.021 Median Lane Width 0.2638 0.0924 0.009 Land Use = Commercial 0.5726 0.1449 0.001 Table 22. Multivariate Model GL 1 D Estimated for NRSNI ALL Collisions Data Points ( N): 22 Degrees of Freedom ( DF): 13 Variable Estimate Standard Error P Value Intercept  1.3999 1.2099  Section Length 0.3479 0.0364 < 0.0001 Average ADT 0.3220 0.0651 < 0.0001 Medtree = 0  0.3673 0.1454 0.015 Posted Speed = 35  0.1005 0.1840 0.143 Posted Speed = 40  0.2853 0.1661 0.143 Median Curb Height 0.0619 0.0293 0.042 Median Lane Width 0.2078 0.0904 0.029 Land Use = Commercial 0.4201 0.1272 0.005 As before, there is considerable consistency in the model parameters common to the other models. The new speed variables ( 85% ile and posted speed) both enter as category variables with the highest speed used as the base. For 85% ile speed, the category “= 40” covers sections in the 35 40 mph 85% ile speed range, while “= 45” covers sections in the 40 45 mph range. This model indicates that lower 85% ile speeds are associated with fewer collisions, compared to the base case of speeds above 45 mph. The second model, which includes posted speed, is less straightforward. Here, 40 mph posted speed is associated with the fewest collisions, and 35 mph has the second fewest, compared to 36 the base case of 45 mph posted speed. On the other hand, the standard errors suggest that the difference between 35 mph and 40 mph posted speeds is not statistically significant. Three other GL 1 models with reasonable statistical properties were estimated using the data set for No Right Side fatal and injury ( F& I) collisions, including intersection collisions. The first of these appears in Table 23 below. Note that no acceptable models could be found for the NRSNI F& I data set with intersection collisions excluded. Table 23. Multivariate Model GL 1 E Estimated for NRS F& I Collisions Data Points ( N): 21 Degrees of Freedom ( DF): 13 Variable Estimate Standard Error P Value Intercept  1.1616 1.3767  Section Length 0.3540 0.0390 < 0.0001 Average ADT 0.3394 0.0838 0.0004 Medtree = 0  0.5913 0.1760 0.0022 Median Width = 10 16  0.2822 0.1694 0.127 Median Lane Width 0.1859 0.1017 0.071 # Lanes = 2 0.3201 0.1657 0.065 Land Use = Commercial 0.2830 0.1472 0.065 This model introduces a new categorical variable for median width. The base value for this variable is Median Width = 16+. Since there are no sections in the data with median widths less than 10 feet and trees, the 0 10 foot median width category was excluded from this estimation. This model is weak statistically in that only a few variables ( section length, ADT, and median trees) are significant at the 95% level. The implications of the model are similar to the model described previously for variables they have in common ( except, of course, this model applies to F& I collisions). In addition, the model implies that roadways with 10 16 foot medians have fewer F& I collisions than medians wider than 16 feet. This seems counter intuitive, but it should be noticed that the median width variable has low statistical significance. The second GL 1 model for No Right Side fatal and injury ( F& I) collisions incorporates 85% ile speed. It appears in Table 24 below. The categorical 85% ile speed variable is defined as before. The apparent association in this model between collisions and speed is hump shaped – where the 35 40 mph category has the fewest collisions, 40 45 mph has the most, and 45 50 mph is in the middle. The contributions of other variables are the same as in previous models. Note that, in this model, the presence of median trees is not quite significant at the 95% level, nor is the 85% ile speed. Table 24. Multivariate Model GL 1 F Estimated for NRS F& I Collisions Data Points ( N): 22 Degrees of Freedom ( DF): 14 Variable Estimate Standard Error P Value Intercept  1.4274 1.2760  Section Length 0.3127 0.0353 < 0.0001 Average ADT 0.2367 0.0667 0.0004 Medtree = 0  0.2667 0.1496 0.072 37 85% ile Speed = 40  0.1937 0.1985 0.054 85% ile Speed = 45 0.2515 0.1535 0.054 Median Lane Width 0.2288 0.0975 0.018 Land Use = Commercial 0.4260 0.1447 0.007 The final GL 1 model estimated using No Right Side fatal and injury ( F& I) collision data is shown in Table 25 below. Table 25. Multivariate Model GL 1 G Estimated for NRS F& I Collisions Data Points ( N): 21 Degrees of Freedom ( DF): 14 Variable Estimate Standard Error P Value Intercept  1.7693 1.4873  Section Length 0.3339 0.0418 < 0.0001 Average ADT 0.4033 0.0859 < 0.0001 Medtree = 0  0.5307 0.1865 0.008 Median Width = 10 16  0.2768 0.1844 0.157 Median Lane Width 0.2321 0.1096 0.040 # Lanes = 2 0.3440 0.1777 0.063 This is the same specification as model GL 1 E ( Table 23) except that land use is not included. As in the previous model, the median width variable has poor statistical significance. The associations are basically the same as the other GL 1 models described in this section. In summary, only eight of the dozens of GL 1 models tested showed acceptable or near acceptable statistical properties. Seven of these are shown in detail above. These models generally seem logical, and all show that there is an association between median trees and an increased number of either total collisions or F& I collisions when the No Right Side data sets are used. Removing collisions that occur at intersections does not appear to affect the results very much. A counter intuitive aspect found in two of the models is that the increase in collisions from having median trees is not mitigated by increased median width. However, it should be noted that data limitations did not permit modeling medians narrower than 10 feet. The possible mitigating aspects of lower section speed were found to be mixed. Finally, it is noteworthy that, despite numerous efforts, no statistically significant associations of the GL 1 model form were found using the data for Left Side Only collisions. The Best Models of Type GL 2 Three GL 2 models were found to with acceptable statistical properties. In two of these, all parameters are significant at the 95% level. In the other, all parameters are significant except for the presence of median trees, which is close to significant. Curiously the three acceptable models were estimated on three different data sets – one each for all No Right Side collisions, F& I No Right Side collisions, and all Left Side Only collisions. No model with acceptable properties could be found using only F& I collisions in the Left Side Only data set. For the sake of comparison, the best model found for the F& I Left Side Only collisions is described, even 38 though the presence of median trees is not significant in this model. Collisions at intersections are included in all the data sets used to fit the GL 2 type models. Cross street density and Land Use appear as significant variables in all three of the models. The number of lanes and posted speed, as well as median curb height appear in two. Median width entered only one model as a significant variable. 85% ile speed was found never to have a significant association in any of the GL 2 models tested. The first GL 2 model appears below in Table 26. It was estimated using the data for all of the No Right Side collisions. All of the categorical variables have been discussed previously, except Cross Street Density, for which the base category is Cross Street Density = M ( medium). In this model, 3 lane and 4 lane directional segments were categorized separately, with # Lanes = 4 used as the base. Table 26. Multivariate Model GL 2 A Estimated for NRS ALL Collisions Data Points ( N): 22 Degrees of Freedom ( DF): 12 Variable Estimate Standard Error P Value Intercept  2.2090 1.2493  Medtree = 0  0.5191 0.1743 0.011 Posted Speed = 35 0.3233 0.1994 0.024 Posted Speed = 40  0.1727 0.1878 “ Cross Street Density = H  0.3541 0.1971 0.015 Cross Street Density = L 0.6584 0.1932 “ Median Lane Width 0.2896 0.1032 0.017 Land Use = Commercial 0.4582 0.1429 0.007 # Lanes = 2  0.5777 0.2521 0.053 # Lanes = 3  0.9584 0.3520 “ As previously noted, the GL 2 models are mathematically equivalent to multinomial models of accident rates. The above model indicates that the accident rate for all No Right Side collisions is higher for sections with median trees ( since the parameter value for Medtree= 0 is negative). The model also implies a U shaped relationship between the accident rate and posted speed – greatest for 35 mph, least for 40 mph, and greater again for 45 mph ( but still below the rate for 35 mph). This is exactly the opposite relationship to that found in one of the GL 1 models. The relationship with cross street density implies that accident rates decrease with increasing cross street density, which is counter intuitive because collisions are known to concentrate at intersections. The roadway width effect is different than found previously – here, three lane directional roadways are associated with the lowest accident rates, followed by two lane roadways, with four lane roadways associated with the highest accident rates. The second GL 2 model, based on F& I No Right Side collisions, is shown below in Table 27. The effects of the different parameters in this model for F& I collisions are mostly similar to the previous model for all collisions ( Table 26). However, the variable for median curb height enters this model and indicates that higher median curbs are associated with fewer collisions, which is the opposite effect found in some of the GL 1 type models. The effect of posted speed changes from U shaped to monotonic, indicating that collisions decrease as section posted speeds 39 increase from 35 to 45 mph. In both models, the highest accident rates are associated with the lowest posted speed category, 35 mph. Table 27. Multivariate Model GL 2 B Estimated for NRS F& I Collisions Data Points ( N): 22 Degrees of Freedom ( DF): 11 Variable Estimate Standard Error P Value Intercept  3.8998 0.9956  Medtree = 0  0.4717 0.1449 0.008 Posted Speed = 35 0.7074 0.1694 0.001 Posted Speed = 40 0.1483 0.1740 “ Cross Street Density = H  0.5217 0.1688 0.001 Cross Street Density = L 0.8404 0.1552 “ Median Lane Width 0.3877 0.0832 0.001 Median Curb Height  0.0637 0.0234 0.017 Land Use = Commercial 0.5049 0.1243 0.002 # Lanes = 2  0.6606 0.2066 0.003 # Lanes = 3  1.3091 0.2967 “ The third GL 2 model with acceptable statistical properties is shown below in Table 28. In this model, estimated for all Left Side Only collisions, the influence of median trees is not statistically significant at the 95% level, although it is close. Other parameters are statistically significant at the 95% level. In this case, the model implies that the accident rate for median width 10 16 feet is higher than for the wider medians. ( This is the opposite of what the GL 1 models indicate.) The implications of other variables are the same as in the previous models. Table 28. Multivariate Model GL 2 C Estimated for LSO ALL Collisions Data Points ( N): 20 Degrees of Freedom ( DF): 13 Variable Estimate Standard Error P Value Intercept  0.6992 0.2302  Medtree = 0  0.2664 0.1598 0.117 Cross Street Density = H  0.2443 0.1592 0.013 Cross Street Density = L 0.5603 0.1941 “ Median Width Cat. = 10 16 0.4689 0.1987 0.035 Land Use = Commercial 0.4528 0.1667 0.017 Median Curb Height  0.1168 0.0460 0.022 Finally, for comparison, Table 29 shows the result of the best GL 2 model estimated using the F& I Left Side Only collisions. Although median lane width and median curb height are close to being significant at the 95% level, the presence of median trees is not at all significant ( P= 0.92). Eliminating the other variables one by one does not change this outcome. 40 Table 29. Multivariate Model GL 2 D Estimated for LSO F& I Collisions Data Points ( N): 22 Degrees of Freedom ( DF): 18 Variable Estimate Standard Error P Value Intercept  4.0240 1.6177  Medtree = 0  0.0171 0.1675 0.920 Median Lane Width 0.2560 0.1369 0.083 Median Curb Height  0.0815 0.0392 0.051 The overall conclusion from the GL 2 modeling is that there is an association between accident rates and the presence of median trees, when all Not Right Side collisions are considered. If the analysis is limited to Left Side Only collisions, a weak association remains between collisions and the presence of median trees ( the presence of median trees is significant at the 80% confidence level). Neither posted speed nor 85% ile speed was found to be significant for “ Left Side Only” collisions. Although posted speed enters as a significant variable for No Right Side collisions, its effect is counter intuitive, slower speeds being associated with more collisions. The Best Models of Type GL 3 Model type GL 3 addresses collision severity by considering the proportion of F& I collisions on the highway sections. Many different model specifications were tested, some of which are shown in Table 17 and Table 18. Three models with acceptable statistical properties were found using data sets that exclude collisions at intersections; while only one acceptable GL 3 model was found when intersection collisions are included. This last model, estimated for Left Side Only collisions, appears in Table 30 below. Table 30. Multivariate Model GL 3 A Estimated for LSO Collisions Data Points ( N): 20 Degrees of Freedom ( DF): 13 Variable Estimate Standard Error P Value Intercept  0.2119 0.1407  Medtree = 0  0.2723 0.0985 0.017 Median Width = 10 16  0.4115 0.0868 0.0005 Cross Street Density = H 0.0246 0.0817 0.014 Cross Street Density = L  0.2924 0.0
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Title  Safety of median trees with narrow clearances on urban conventional highways 
Subject  Traffic safetyCalifornia.; Median strips.; Roadside plantsCalifornia.; TreesCalifornia. 
Description  Text document in PDF format.; Cover title.; Title from PDF title page (viewed on January 16, 2009).; Performed by for California Dept. of Transportation, Traffic Operations Program.; "March 2004."; Phase III final report. 
Creator  Sullivan, Edward C. 
Publisher  Cal Poly State University, Applied Research and Development Facility 
Contributors  California. Dept. of Transportation. Traffic Operations Program.; California Polytechnic State University, San Luis Obispo. Applied Research and Development Facility. 
Type  Text 
Identifier  http://ceenve3.civeng.calpoly.edu/sullivan/Trees/phase_iii_reportfinal.pdf 
Language  eng 
Relation  http://worldcat.org/oclc/298571460/viewonline 
DateIssued  [2004] 
FormatExtent  vii, 94 p. : digital, PDF file (3.25 MB) with col. charts. 
RelationRequires  Mode of access: World Wide Web. 
Transcript  Safety of Median Trees with Narrow Clearances on Urban Conventional Highways Phase III Final Report Submitted to: State of California Department of Transportation Traffic Operations Program Sacramento, CA 94273 Submitted by: Edward C. Sullivan, Principal Investigator Applied Research and Development Facility Cal Poly State University San Luis Obispo, CA 93407 March 2004 ABSTRACT This is the final report for the third phase of a Caltrans sponsored study to investigate the safety of placing large trees with narrow side clearance in medians of conventional state highways that also serve as principal urban streets. Although the study focused on trees in medians, the effects of many other roadside features were also considered. Previous phases of this study produced a literature search and contacts with experts in the field to identify and document what was already known about urban street trees and collisions. Data were then collected and analyzed for 65 conventional urban highway sections with medians, including facilities under both state and local jurisdiction, as well as with and without curbed medians. Statistical methods were used to explore quantitative relationships between both total collisions and fatal and injury ( F& I) collisions on these highway sections as influenced by various geometric, traffic and environmental conditions. The objective was to isolate the possible impacts of large median trees on collision rates and severity, and to determine the conditions that might mitigate or exacerbate any such impacts. The general conclusion of these initial investigations was that, for the highway sections considered, the presence of large median trees does consistently correlate with higher total accident rates, although differences observed in fatal and injury accident rates were generally not statistically significant. In addition, neither lower posted speeds nor increased side clearances to median trees were shown to be associated with reduced accidents. The detailed findings from this part of the investigation are provided in a separate Phase II report. 1 Phase III of the study dug further into the relationships found previously, and refined the study output in a number of important ways. First, the sites considered were limited to only highways under state jurisdiction and to only highways with curbed medians, in order to provide a more homogenous data set. In addition, the statistical modeling was modified to focus on collisions that occurred in or near the median area, as well as collisions located away from intersections. The data set was also expanded to include additional variables, including measured speeds and Caltrans rate group designations. Finally, additional model types not employed in Phase II were applied in the search for significant associations, and selected printed collision reports were examined in an effort to identify possible effects of trees not evident in the quantitative data. The conclusion of the Phase III investigation is that large trees planted in curbed medians along conventional urban and suburban state highways are associated with more collisions and with increased collision severity, however for some collision types the statistical associations are weak. The strengths of the associations found are summarized below. Strength of the Association Between Collisions and Median Trees in ⇒ Total # of Collisions # of F& I Collisions % of F& I Collisions Interior Lanes, Median Area & Beyond Significant Significant Significant Collision Locations Only Median Area & Beyond Weak Weak Significant Study findings show that increasing median width does not reduce collision expectations, and that the effects of speeds are mixed. 1 Safety of Trees with Narrow Clearances on Urban Conventional Highways: Phase II Final Report. Applied Research and Development Facility, Cal Poly State University. February 2003. Internet, on line at: http:// ceenve. calpoly. edu/ sullivan/ trees/. iii ACKNOWLEDGMENTS This report results from the efforts of an interdisciplinary team composed of the following faculty and students at Cal Poly State University: James Daly, Faculty Member, Statistics Karthikeyan Dhandapani, Graduate Assistant, Civil and Environmental Engineering Laine Elliott, Student Assistant, Statistics Brendon Finnecy, Student Assistant, Civil and Environmental Engineering Travis Hurt, Student Assistant, Civil and Environmental Engineering Eugene Jud, Faculty Member, Civil and Environmental Engineering Justin Link, Student Assistant, Civil and Environmental Engineering Danielle Ringstmeyer, Student Assistant, Civil and Environmental Engineering Edward Sullivan, Faculty Member, Civil and Environmental Engineering The study team was augmented by a panel of distinguished technical advisors: Professor Emeritus Ezra Hauer of the University of Toronto, Professor Emeritus Robert Layton of Oregon State University, and Professor Richard McGinnis of Bucknell University. We appreciate their valuable insights in the development of the study methodology and their comments regarding the draft final report. We appreciate the guidance and assistance of Phil Jang, the study’s technical monitor for Caltrans, of Mike Gray, Lyle Oehler, and Jack Boda, who provided suggestions and administrative assistance throughout the study, and of Janice Benton, of the Caltrans TASAS Unit, who helped us with many aspects of data collection. We are also very grateful for the help received from numerous other Caltrans headquarters and district office staff members throughout the state who helped us with suggestions and with assistance in data collection. Our additional thanks to dozens of local public works staff throughout California who assisted us in generously contributing their time and effort to provide needed traffic and roadway data. DISCLAIMER The contents of this report reflect the views of the authors who are alone responsible for the findings and accuracy of the information presented herein. The contents do not necessarily reflect the official views or policies of the State of California. The report does not constitute a standard, specification or regulation. iv Safety of Median Trees with Narrow Clearances on Urban Conventional Highways: Phase III Final Report TABLE OF CONTENTS ABSTRACT....................................................................................................................... ......... iii DISCLAIMER..................................................................................................................... ......... iv TABLE OF CONTENTS............................................................................................................... v LIST OF FIGURES...................................................................................................................... vi LIST OF TABLES........................................................................................................................ vi 1. Introduction and Executive Summary................................................................................... 1 1.1 Background..................................................................................................................... .. 1 1.2 Overview of Methodology................................................................................................. 3 1.3 Summary of Findings...................................................................................................... 10 1.4 Overview of the Rest of the Report................................................................................ 12 2. Development of the Phase III Data Set................................................................................ 13 2.1 Chapter Introduction....................................................................................................... 13 2.2 Sampling Considerations............................................................................................... 13 2.3 Coding of Highway Section Characteristics................................................................. 17 2.4 Coding of Collision Data................................................................................................. 19 3. Results from Modeling Based on TASAS Collision Data.................................................. 23 3.1 Chapter Introduction....................................................................................................... 23 3.2 Generalized Linear Modeling.......................................................................................... 23 3.3 Estimation of Simple Accident Rates............................................................................ 45 3.4 Tests for Differences in Collision Characteristics........................................................ 52 4. Results from Additional Investigations.............................................................................. 59 4.1 Chapter Introduction....................................................................................................... 59 4.2 Review of Selected Printed Collision Reports.............................................................. 59 4.3 Findings from Field Investigations of Collision Concentrations................................ 65 4.4 Investigation of Differences between Posted Speeds and Measured Speeds........... 73 4.5 The Modeling Implications of Differences Between SWITRS and TASAS................. 76 5. Conclusion and Recommendations.................................................................................... 81 Appendix A – Example Data for Study Sections with Median Trees.................................... 85 Appendix B – List of Study Sections without Median Trees................................................. 87 Appendix C – Section Photos.................................................................................................. 89 Appendix D – Photos of Intersections with Collision Concentrations................................ 93 v LIST OF FIGURES Figure 1. Printed Collision Reports  Breakdown of Median Types............................................ 60 Figure 2. Collisions Reports: Severity Breakdown by Median Type........................................... 61 Figure 3. Collisions Reports: Overall Collision Type Breakdown by Median Type..................... 61 Figure 4. Concentration of Collisions on 04 ALA 123 ( Berkeley)............................................... 67 Figure 5. Concentration of Collisions on 12 ORA 039 ( Buena Park).......................................... 67 Figure 6. Concentration of Collisions on 07 LA 066 ( Claremont)............................................... 68 Figure 7. Concentration of Collisions on 04 ALA 238 ( Hayward)............................................... 68 Figure 8. Concentration of Collisions on 12 ORA 039 ( Huntington Beach)................................ 69 Figure 9. Concentration of Collisions on 07 LA 066 ( La Verne)................................................. 69 Figure 10. Concentration of Collisions on 04 SM 081 ( South San Francisco)........................... 70 Figure 11. Measured Distances from End of Median to First Tree............................................. 71 Figure 12. SR 123 at Addison St. ( Berkeley) ( 15 m. to First Median Tree)................................ 72 Figure 13. SR 66 at Indian Hill Blvd. ( Claremont) ( 35 m. to First Median Tree).......................... 72 Figure 14. SR 66 at East Mountain ( Claremont)......................................................................... 73 Figure 15. SR 66 at Towne Ave. ( Claremont)............................................................................. 73 Figure 16. Comparison of Posted Speeds and 85% ile Speeds.................................................. 75 Figure 17. Comparison of Posted Speeds and Top of Pace Speeds......................................... 76 LIST OF TABLES Table 1. The Study Data Set at a Glance..................................................................................... 4 Table 2. Principal Highway Characteristics Considered in the Phase III Study............................ 6 Table 3. Average Characteristics of Highway Sections with and without Median Trees.............. 7 Table 4. Collision Characteristics Considered in the Phase III Analysis....................................... 7 Table 5. MVM of Exposure by Posted Speeds, ADT, and Median Trees................................... 14 Table 6. MVM of Exposure by Posted Speeds Combined with ADT, and Median Trees........... 14 Table 7. MVM of Exposure by Median Width and Setback to Median Trees.............................. 15 Table 8. MVM of Exposure by Median Width Combined with Speed, and Median Trees........... 15 Table 9. MVM of Exposure by Speed and ADT Combined with Setback to Median Trees........ 16 Table 10. MVM of Exposure by Rate Group Combined with Median Width, and Median Trees16 Table 11. MVM of Exposure by Rate Group Combined with ADT Category, and Median Trees17 Table 12. Coding of Highway Section Characteristics................................................................ 17 Table 13. Significance of Initial Models for All “ No Right Side” Collisions.................................. 25 Table 14. Significance of Initial Models for F& I “ No Right Side” Collisions................................ 26 Table 15. Significance of Initial Models for All “ Left Side Only” Collisions.................................. 28 Table 16. Significance of Initial Models for F& I “ Left Side Only” Collisions................................ 29 Table 17. Summary of Multivariate Models with Intersection Collisions Included....................... 31 Table 18. Summary of Multivariate Models with Intersection Collisions Excluded..................... 33 vi Table 19. Multivariate Model GL 1 A Estimated for NRS ALL Collisions.................................... 34 Table 20. Multivariate Model GL 1 B Estimated for NRSNI ALL Collisions................................ 35 Table 21. Multivariate Model GL 1 C Estimated for NRSNI ALL Collisions................................ 36 Table 22. Multivariate Model GL 1 D Estimated for NRSNI ALL Collisions................................ 36 Table 23. Multivariate Model GL 1 E Estimated for NRS F& I Collisions.................................... 37 Table 24. Multivariate Model GL 1 F Estimated for NRS F& I Collisions..................................... 37 Table 25. Multivariate Model GL 1 G Estimated for NRS F& I Collisions.................................... 38 Table 26. Multivariate Model GL 2 A Estimated for NRS ALL Collisions.................................... 39 Table 27. Multivariate Model GL 2 B Estimated for NRS F& I Collisions.................................... 40 Table 28. Multivariate Model GL 2 C Estimated for LSO ALL Collisions.................................... 40 Table 29. Multivariate Model GL 2 D Estimated for LSO F& I Collisions..................................... 41 Table 30. Multivariate Model GL 3 A Estimated for LSO Collisions........................................... 41 Table 31. Multivariate Model GL 3 A Re Estimated Without Section 08 SB 083....................... 42 Table 32. Multivariate Model GL 3 B Estimated for LSONI Collisions........................................ 43 Table 33. Multivariate Model GL 3 C Estimated for NRSNI Collisions....................................... 43 Table 34. Multivariate Model GL 3 D Estimated for NRSNI Collisions....................................... 43 Table 35. Left Side Accident Rates Stratified by Presence/ Absence of Median Trees.............. 46 Table 36. Left Side Accident Rates Stratified by Rate Group..................................................... 47 Table 37. Left Side Accident Rates Stratified by Average Daily Traffic...................................... 48 Table 38. Left Side Accident Rates Stratified by 85% ile Speed................................................. 49 Table 39. Left Side Accident Rates Stratified by Posted Speed................................................. 49 Table 40. Left Side Accident Rates Stratified by Number of Directional Lanes.......................... 50 Table 41. Left Side Accident Rates Stratified by Median Width................................................. 50 Table 42. Left Side Accident Rates Stratified by Setback to Median Trees............................... 51 Table 43. Left Side Accident Rates Stratified by Tree Trunk Diameter...................................... 52 Table 44. Comparison of Overall Collision Types for All Collisions............................................ 53 Table 45. Comparison of Overall Collision Types for Fatal and Injury Collisions....................... 54 Table 46. Comparison of Objects Hit for Collisions in the “ Left Side Only” Data Set................. 54 Table 47. Comparison of Collision Types for All Left Side Collisions by Posted Speed............. 55 Table 48. Comparison of Collision Types for F& I Left Side Collisions by Posted Speed........... 55 Table 49. Surface Conditions for Left Side Collisions with and without Median Trees............... 56 Table 50. Lighting Conditions for Left Side Collisions with and without Median Trees............... 56 Table 51. Violations Cited for Left Side Collisions with and without Median Trees.................... 56 Table 52. Number of Parties Involved for Left Side Collisions with and without Median Trees.. 57 Table 53. Collision Statistics Used to Screen Collision Concentrations for Further Investigation................................................................................................................ 66 Table 54. Coverage of Available Speed Zone Study Data......................................................... 74 Table 55. Comparisons of TASAS and SWITRS Data Sets for Equivalent Highway Sections... 77 vii 1. Introduction and Executive Summary 1.1 Background The California Department of Transportation ( Caltrans) Traffic Operations Program asked California Polytechnic State University ( Cal Poly) to perform a study of the safety of trees with limited side clearance in medians of urban and suburban conventional highways. The study was motivated by the need to develop a better empirical foundation on which to base agency policy for responding to local community requests for planting additional median trees. The study focused on estimating statistical associations between the number and severity of collisions and the presence of median trees. The influence of many other design and environmental features were also taken into consideration. The overall study was conducted in three phases, funded and conducted sequentially: Phase I – An investigation to determine what was already known about traffic safety and urban street trees, using the techniques of literature search and contacts with pertinent organizations and experts. In addition, this phase established the technical approach to the work conducted in Phase II. Phase II – An initial statistical investigation of broad cross sectional relationships between collision experience and the presence of trees in urban and suburban conventional highway medians. The purpose was to see if significant differences in collision experience are statistically associated with the presence of median trees and, if so, to identify the factors that might mitigate or exacerbate that association. The results of the Phase I and Phase II investigations appear in an earlier report. 2 Phase III – Further in depth investigations, primarily of a cross sectional statistical modeling nature, to refine and extend the data set and modeling of Phase II, and to address certain unanswered questions that remained at the close of the earlier investigation. This is the final report for Phase III of the study. It extends but does not supercede the Phase II report issued previously. The Phase III investigation, which is the subject of this report, addressed collision experience for the following highway types: Highways in urban and suburban settings that serve a mix of through and local access traffic ( rural highways were not considered). Conventional highways, that is, highways without access control except as determined by local land development practices. Highways within the state highway system, owned and managed by the California Department of Transportation. Highways likely to be viewed as local arterials ( as opposed to collectors or locals). Highways with curbed raised medians, both with and without median trees ( to permit comparison). 2 Safety of Trees with Narrow Clearances on Urban Conventional Highways: Phase II Final Report. Applied Research and Development Facility, Cal Poly State University. February 2003. Internet, on line at: http:// ceenve. calpoly. edu/ sullivan/ trees/. For these highway types, site characteristics, such as roadway widths, lane widths, median widths, setbacks, traffic volumes, speeds, and surrounding development types, vary widely. The State’s TASAS3 data system was used to identify all highway sections in the California highway inventory with the desired combinations of physical characteristics. Suitable candidate sections were defined as highway sections matching the above criteria, where geometric characteristics and other relevant road conditions remain mostly unchanged for about a mile or more. It was felt that study sections needed to be at least about a mile long in order to avoid excessive random variation in collision experience relative to the average. The suitability ( that is, the homogeneity) of each apparently suitable candidate study section was verified by a site visit during which numerous site measurements were obtained. These site visits resulted in eliminating some locations that were unsuitable due to lack of homogeneity or other apparent reasons. In a few cases, additional highway sections with suitable characteristics were discovered during the site visits. Some candidate sections were subsequently eliminated for other reasons, for example where we later determined that median trees were planted too recently to match the coverage period of the collision data. The final Phase III data set, created by combining new section data with suitable state highway sections remaining from Phase II, contains nineteen state highway sections with large median trees and ten state highway sections with raised curbed medians without trees. “ Large” trees are defined as trees with trunk diameters 100 mm ( 4 inch) or more at a point 1.2 m. ( 4 feet) above the ground. The final data set contains most of the potentially suitable candidate state highway sections in California of sufficient length, and virtually all of the suitable candidate sections within the major urban areas of Northern and Southern California ( Caltrans Districts 04, 07, 08, 11, and 12). A small number of potentially suitable sections located in the Central Valley and far north in the San Francisco Bay Area were not included due to travel inconvenience and the belief that the highway sections already available were a sufficiently large and representative data set for the intended analysis. Note that two of the nineteen median tree sections with posted speeds of 50 mph or more were excluded from most of the statistical analyses, since they were considered not entirely representative of the highway types of interest. Collision data were obtained for all study sections for the six year period from January 1996 through December 2001. Analogous to the one mile minimum adopted for section length, six years was considered an appropriate period to eliminate excessive random variation in the collision data. Local authorities were contacted to determine that for all the candidate sections with median trees, the trees had been in place at least since 1996. The corresponding traffic volumes for each section were obtained from a Caltrans web site, 4 and field measurements of vehicle speeds were obtained, where available, from the Caltrans district offices. Adequate field speed data to characterize traffic conditions during 1996 2001 were available for 27 of the 29 highway sections in the final data set. An extensive statistical analysis was undertaken, using several different model forms to examine the possible relationships between collisions, the presence of nearby “ large” trees, and other roadway, traffic, and environmental characteristics. The statistical analysis examined relationships in both the number and severity of collisions. One can hypothesize that, all else being equal, the number of collisions might be affected by median trees because nearby trees may restrict visibility, especially at intersections, or because driver behavior and surface friction might be affected by shadows or detritus on the road surface. One can also hypothesize that 3 TASAS = Traffic Accident Surveillance and Analysis System. 4 At http:// www. dot. ca. gov/ hq/ traffops/ saferesr/ trafdata/ 2 severity might be affected because large trees are unyielding fixed objects, consistently shown to be among the most harmful of all roadside objects to hit. On the other hand, there may also exist countervailing positive safety benefits from trees due to traffic calming, reduction of glare, blocking of cross median collisions, and control of runoff and erosion. Although this study addressed many relationships between median street trees and traffic safety, some things were not considered. For example, the study did not directly consider the increased risks to road crews in maintaining median vegetation, other maintenance costs that might result due to pavement damage from root growth, or possibly enhanced pavement life from shading. This study was never intended to provide a comprehensive benefit cost assessment of all aspects of planting median trees along urban and suburban conventional state highways. Rather, it is a focused examination of the safety consequences of median trees, based on a substantial data set of historical collision data. It should be noted that the statistical models developed in this study are strictly cross sectional. They estimate how differences in roadway characteristics, with and without median trees, are related to differences in accident rates by comparing similar but different highway sections. While before after comparisons of particular highway sections could provide substantial additional insights, time constraints and data limitations did not accommodate making before after site specific comparisons. Finally, it should be noted that our data set consists entirely of urban and suburban roadway sections in large urban areas of California. Thus, these findings are not necessarily applicable to the design types and driver populations found elsewhere. The following sections provide an overview of the study methodology and a summary of the principal findings. The details of the work are presented in the other chapters and appendices. 1.2 Overview of Methodology The principal methodology for Phase III of this study was to apply a variety of statistical modeling approaches to examine relationships between collisions, median trees, and other roadway characteristics. In addition, several parallel investigations of a non modeling nature were performed to produce additional insights into the problem at hand. The study methodology was motivated and informed by findings from the literature review and contacts with experts in the field. The literature review, from Phase I of the study, shows that while it is well established for rural highways that unprotected trees near the traveled way substantially increase collisions and their severity, there is little direct empirical evidence on this issue available for urban and suburban conventional arterials. What little evidence does exist presents conflicting conclusions. The specific components of the methodology for this study are: Expanded data collection for study sections on state highways. Statistical Modeling: • Generalized linear modeling of relationships between total and fatal and injury ( F& I) collisions and roadway characteristics ( three distinct model structures were applied), • Estimation and comparison of simple accident rates and their confidence intervals, • Tests of differences in collision characteristics, with and without median trees. Supplemental Investigations: • Review of selected original collision reports – narratives and other details, • Field investigations of possible visibility limitations near selected collision clusters, 3 • Examination of differences in posted speeds and measured speeds for the selected highway sections, and their implications for statistical modeling, • Assessment of differences in collision data between TASAS and SWITRS ( as follow up to Phase II). The data collection plan was guided by the need to have acceptable statistical properties for the accident models to be developed. We used a rule of thumb that we should seek at least 250 million vehicle miles ( MVM) of exposure for key combinations of the principal section variables of concern, specifically median type ( trees or no trees) combined with the rate group, the posted speed, and the median width category. The 250 MVM threshold would permit us to estimate the overall fatal and injury accident rates in each category within about a 12.5% expected error at 95% statistical confidence. 5 Table 1. The Study Data Set at a Glance State Highways With Median Trees Without Median Trees Total Number: 19 10 29 Sections: Total Mileage 40.5 17.8 58.3 MVM of exposure ( in 6 yrs.) 3268 2055 5323 Total 10563 3720 14283 Fatal & Injury 4334 1746 6080 All Collisions: Fatal 34 14 48 Total 6826 2761 9587 Fatal & Injury 2998 1384 4382 Right Side Collisions Eliminated: Fatal 29 14 43 Total 1648 706 2354 Fatal & Injury 759 396 1155 Left Side ( Median) Collisions Only: Fatal 7 5 12 Total 4328 1842 6170 Fatal & Injury 1865 859 2724 Right Side & Intersection Collisions Eliminated: Fatal 22 9 31 Total 597 242 839 Fatal & Injury 265 125 390 Left Side ( Median) Collisions Only; No Intersections: Fatal 3 2 5 5 95% statistical confidence is widely used in exploratory statistical studies of this nature. A higher level, say 99%, would result in fewer comparisons being judged statistically significant; a lower level would result in more comparisons being judged significant. 4 Upon applying the various selection criteria, twenty nine California state highway sections were identified with which to perform the Phase III statistical analysis. The overall features of these twenty nine sections are summarized in Table 1 above. Table 1 shows that there are nearly twice as many sections with median trees as without trees, and more than twice the mileage; however, the sections with median trees have only about 60% more exposure ( MVM) than the sections without trees. This reflects the fact that, on average, the sections without trees have more traffic ( the average ADT is 36,150 for sections with median trees compared to 49,127 for sections without). There are also many other differences among the characteristics of the twenty nine sections, and in their collision experience. Table 1 also shows collision counts for the six year analysis period, broken down by total collisions, fatal and injury ( F& I) collisions, and fatalities only. Collision counts are further grouped by where on the highways the collisions occurred. Of the five sets of counts shown, the first set includes all reported collisions on the state highway sections as reported in the State’s TASAS database. 6 The second set excludes collisions described as occurring entirely on the right side of the highway, defined as the right lane, the right shoulder, or beyond. The third set is more selective; including only collisions having some reported impact in the left ( median) shoulder area, the median, or beyond. The fourth and fifth data sets are the same as the second and third, except collisions located at intersections are not included. The statistical modeling for Phase III focused entirely on the second through fifth data sets, excluding collisions occurring entirely on the right side. Initially, whether or not to include collisions at intersections was questioned. On the one hand, collisions typically cluster at intersections where operations are dominated by factors related to accommodating turning conflicts. This argues for ignoring intersection collisions. On the other hand, if median trees are planted close to intersections, they might impact sight distances and, consequently, collision experience. Although investigations made during the study show that intersection sight distances are generally not restricted by median trees for the highways in our data sets, it was decided to perform statistical modeling both with and without intersection collisions. A quick look at Table 1 suggests that the presence of trees in medians is not associated with dramatic differences, although some differences are evident. Of 2354 left side collisions in the data set, only 12 are fatalities, although nearly 50% ( 1143) involve injuries. While sections with median trees represent 69% of the total mileage and 61% of the total exposure ( MVM), 58% of the left side fatalities occurred on sections with median trees. 7 On the other hand, 66% of the injury collisions and 70% of all left side collisions occurred on sections with median trees. If intersection collisions are excluded, 68% of the left side injury collisions and 71% of all left side collisions occurred on sections with median trees. Clearly, the possible associations between median trees and the number of accidents, and the injury accidents in particular, warrant in depth investigation. This report examines these associations in detail and assesses their statistical significance. In reading the findings of this analysis, it is important to recognize, as shown in Table 1, that the magnitude of the consequence in terms of increased collisions, especially increased fatal and injury collisions, is fairly small. This is noteworthy because, as mentioned previously, the highway sections in our data set represent the majority of urban 6 Collisions reported as occurring on cross streets near but not on the actual state highway were eliminated. 7 As small numbers, fatality percentages are highly variable – for example, one additional fatality in a section with trees would result in 61% of fatal collisions being on sections with trees. 5 conventional state highway sections in California of substantial length that have curbed medians. Information was coded for numerous physical, traffic, and environmental characteristics of highway sections thought potentially to be related to differences in their collision experience. Several additional data items, tested and found to be insignificant in the Phase II analysis, also appear in the data set but were generally not used in this part of the study. The principal characteristics considered in the Phase III statistical analysis are listed in Table 2 below. Table 2. Principal Highway Characteristics Considered in the Phase III Study Median Trees or Not# Section Length Average Daily Traffic Posted Speed Average Speed Critical ( 85% ile) Speed Top and Bottom of Pace Speed Range % Observations in 10 mph Pace Range Number of Lanes Rate Group Total Median Width Median Curb Height Median Shoulder Width Setback – Curb to Median Trees Setback – Traveled Way to Median Trees Median Tree Trunk Diameter Regularity of Median Tree Alignment# Right Curb Height Right Shoulder Width Right Side Trees or Not# Setback – Curb to Right Side Trees Right Side Utility Poles or Not# Right Side Parking or Not# Right Side Sidewalks or Not# Highway Curvature# Highway Grades# # 1 Lane Width Right Lane Width Adjacent Land Use# Cross Street Density# # Coded only as category variables, such as High/ Medium/ Low, Yes/ No, etc. Other derivative variables were generated during the analysis, usually by transforming continuous variables, such as ADT, median width, etc., to categorical variables in order to avoid having to make inappropriate assumptions regarding the linearity of their effects. As noted, the study objective was to try to determine conclusively whether or not the presence of large median trees is systematically associated with differences in the number or the severity of collisions on conventional urban highways. This was done primarily by comparing statistical associations for the sections with and without median trees. However, it should be noted that the selected highway sections also differ in other ways, which might also be associated with differences in their collision experience. Some of these differences are shown below in Table 3. A goal of statistical modeling is to try to sort out the differences associated with the characteristic of interest ( median trees) from any differences due to other factors, however this cannot always be done completely. Collision characteristics extracted from the statewide TASAS data base for each highway section are shown below in Table 4. As previously noted, these characteristics were extracted for five different data sets of collisions: ( 1) all collisions that occurred on the highway section; ( 2) all collisions except those involving only the right side of the highway; ( 3) all collisions involving only the median shoulder or beyond; ( 4) collisions excluding those located only on the right side of the highway or at intersections; and ( 5) collisions involving only the median shoulder or beyond and that are not at intersections. 6 Table 3. Average Characteristics of Highway Sections with and without Median Trees Section Characteristic Average for the 19 Sections with Median Trees Average for the 10 Sections without Median Trees Section Length ( miles) 2.7 1.8 Posted Speed ( mph) 38.4 40.5 85% ile Speed ( not all sections) 41.9 44.0 2001 Average Daily Traffic 36,774 50,459 Number of Directional Lanes 2.1 2.8 Median Width ( feet) 22.0 14.2 Median Shoulder ( feet) 0.7 0.5 Median Curb Height ( inches) 6.1 6.0 # 1 ( Median) Lane Width ( feet) 11.9 11.2 Right side Shoulder ( feet) 6.9 6.6 Six Year Exposure ( MVM) 172 206 Table 4. Collision Characteristics Considered in the Phase III Analysis Six Year Collision Counts: Total Collisions, Injury Collisions, Fatal Collisions Collision Type: Hit Object, Head On, Rear End, Sideswipe, Broadside, Hit Pedestrian# Object Struck: Tree, Sign or Pole, Guardrail or Barrier, Curb or Island# Violation: Under Influence, Following Too Close, Speeding# Surface Condition: Dry, Slippery, Wet, Snow or Ice# Road Condition: Nothing Unusual, Holes/ Ruts, Loose Material, Construction Reduction# Weather: Clear, Cloudy, Rain, Fog# Lighting: Daylight, Dusk, Darkness# # Separate breakdowns were produced for all accidents in the group, and for fatal and injury accidents independently. Appendices A and B show additional details about the highway section data set. The complete study data set is available on line at: http:// ceenve. calpoly. edu/ sullivan/ trees/ Statistical modeling was performed using SAS ( the Statistical Analysis System) and Excel. This included three types of generalized linear modeling, calculation of simple accident rates ( for total and fatal & injury collisions), and chi square tests of differences in collisions characteristics. Three forms of generalized linear models were tested with a wide range of candidate explanatory variables. These three model forms are shown below. In the equations, COLLi is 7 the observed annual number of collisions on highway section i; 8 Li is the section length; ADTi is the section average daily traffic; MEDTREEi is either 0 or 1, indicating whether section i has median trees; ε is the base of the natural logarithms (≈ 2.718); Xi1, Xi2, etc. are other section characteristics taken from Table 2; β0, β1, β2, etc. are parameters obtained from fitting the model to the data; and ERRi is the error term accounting for random effects not explicitly considered in the model. Model GL 1: iXXMEDTREEADTLiERRCOLLiiiii)(... 25143210++++++= ββββββε ( this error term ERRi is assumed to follow the negative binomial distribution) Model GL 2: iXXMEDTREEiiiERRADTLCOLLiii)(... 231210++++= ββββε ( this error term ERRi is assumed to follow the Poisson distribution) Model GL 3: iXXMEDTREEALLiIFiERRCOLLCOLLiii)()(... & 231210++++= ββββε ( this error term ERRi is assumed to follow the Poisson distribution) Models GL 1 and GL 2 were used to establish possible associations between the number of collisions in one of the five collision data sets and various section characteristics. For these models, some included all collisions, while others included fatal and injury only. Model GL 1 is considered a superior specification because it can capture the potential differences in collision experience associated with differences in the section ADT. Model GL 2, which is algebraically equivalent to modeling the section accident rate, is included for continuity with the work completed in Phase II. Model GL 3 is designed to examine accident severity, expressed as the proportion of fatal and injury collisions on each section. Simple accident rates were also estimated and compared. Since accident rates are generally based on simple stratifications and ignore possible relationships to section lengths and ADT levels, this approach is inherently inferior to multivariate modeling. However, as long as the limitations are recognized, accident rates are easily understood and potentially able to provide useful insights. Accident rates for all collisions and for F& I collisions in each of the five data sets were calculated separately for highway sections stratified by various characteristics, with and without median trees, using the following expression: () ΣΣΣΣ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛ = iyiyyiiyiyADTNLAR610 where: R is the average accident rate ( accidents per million vehicle miles), Aiy is the number of collisions observed on section i in year y, Li is the length ( in miles) of section i, Ny is the number of days of accident counts in year y ( usually 365), 8 In some models, COLLi and ADTi are the actual annual values for the six year observation period while, in other models, COLLi and ADTi are averages for the entire six year period. 8 ADTiy is the average daily traffic, in vehicles per day, for section i in year y, 106 is a scaling factor so R is in accidents per million vehicle miles ( MVM). Accident rates are presented with estimated 95% (±) confidence intervals obtained from: MVMR96.1=± where: MVM is the exposure in millions of vehicle miles associated with the estimated accident rate ( the denominator of the previous expression divided by the 106 scaling factor) The confidence interval formula follows directly from assuming that the number of collisions is a random variable that follows the Poisson distribution. Finally, chi square tests were used to explore if distributions of collision characteristics are significantly different with and without the presence of median trees, and with variations in other section characteristics. The corresponding test statistic is: () Σ− = kkkkEEO22χ where: χ2 is the Chi Square test statistic, Ok is an observed collision count within the distributions being compared, Ek is the corresponding expected count assuming both distributions match in their row and column totals. A large enough value of the test statistic χ2 allows us to reject the null hypothesis that the two distributions of collision characteristics are not significantly different. The methodologies used to carry out the four additional non modeling investigations conducted during Phase III were as follows: 1. The collision data for our highway sections were filtered in order to identify a subset of approximately 100 collisions that appeared especially important with regard to the possible influence of median trees. Targeted collisions were those involving incursion into the median shoulder or beyond, and one or more of the following: a fatality was involved. a tree or other median vegetation was hit, a pedestrian was hit, another vehicle was hit head on. Since the number of collisions with these specific characteristics was limited, some additional left side collisions were randomly selected from cases where injuries or where hitting posts and poles were involved. Caltrans district offices provided photocopies of the original collision reports for these selected collisions, and these reports were carefully scrutinized to understand the role of median trees with regard to their possible influence on each collision and its severity. 2. The collision data for our highway sections with trees were analyzed to identify noteworthy collision clusters. These clusters usually occurred in the vicinity of intersections. Selected 9 locations were re visited to make sight distance measurements, in order to see if visibility problems were evident and, if so, whether the presence of trees might be related. 3. Phase II of the study developed a number of statistical models that, for convenience, were based entirely on section posted speeds. In Phase III, measured section speed data were obtained and key speed measurements, such as critical ( 85% ile) speed and top of pace speed, were also used in the statistical modeling. A question remaining from Phase II is whether the use of actual speeds would make much difference in the findings. Consequently, an investigation was performed to compare section posted speeds with measured speeds, and to interpret any differences with respect to their implications for collision modeling. 4. The Phase II statistical modeling was based on 65 highway sections, including portions of state highways and local facilities considered to have similar characteristics. In order to do this, it was necessary to use two different sources of collision data: the TASAS data base for the state highway sections, and the California Highway Patrol’s SWITRS data base for the local facilities. 9 Although there is much similarity in the data in these two data systems, there are also some differences that raised concern that the findings of the Phase II modeling could have been impacted by inconsistencies in the two data sets. Consequently, an additional investigation was performed to assess the differences in the TASAS and SWITRS data sets for a number of selected state highway sections, and to explore the implications of any differences for the previously developed Phase II models. The major findings of these analyses are summarized in the following section. The results are documented in detail in the later chapters of this report. 1.3 Summary of Findings The principal conclusion from Phase III of this study is that large trees planted in curbed medians along conventional urban and suburban state highways are associated with more total collisions and more fatal and injury collisions, at the 95% level of statistical confidence, when collisions occurring only on the right side of the highway are excluded from consideration. In addition, collision severity ( measured by the proportion of F& I collisions) is significantly higher in the presence of median trees. When collisions are further limited to only those involving the median shoulder, the median, or beyond, a significant association continues to be found between the presence of median trees and severity. However, one highway section in the data set with an unusually high proportion of F& I collisions probably contributes disproportionally to the strength of this association. Only weak associations were found between median trees and the frequency of left side collisions. Nevertheless, based on all the evidence, we conclude that some association does exist between left side collisions and median trees. These findings hold across a wide range of highway types, including posted speeds ranging from 35 to 45 mph and a variety of median widths. These findings generally hold whether or not collisions occurring at intersections are included. In presenting these findings, we should clarify that “ significant” means “ statistically significant at the 95% confidence level.” A difference is regarded as statistically significant if it would appear less than 5% of the time due to random variation in the sample data, when in reality no difference would exist if we used the data for 100% of the highways of concern ( not just a 9 SWITRS = Statewide Integrated Traffic Records System, while TASAS = Traffic Accident Surveillance and Analysis System. 10 sample of them). When a difference is found not to be statistically significant, it is not proof that the difference in question does not exist. Rather, it means that the data do not support with 95% confidence the conclusion that the difference exists. Statistical methods of this type cannot demonstrate conclusively that something does not exist. In addition, we should recognize that differences found not to be significant at the 95% confidence level are sometimes statistically significant at lower confidence levels. 10 While the presence of median trees is generally associated with increased accidents and greater severity, other characteristics of the highway sections interact in complex and sometimes unexpected ways. Specifically, it was found that the number of collisions and collision severity usually decrease in association with lower actual ( 85% ile) section speeds but, in most cases, collisions increase in association with lower posted speeds. While simple accident rates are usually higher in the presence of median trees, the increase in accident rates is less for sections with 40 45 mph 85% ile speeds than for sections with 35 40 mph speeds. It was also found, counter intuitively, that the number of collisions and collision severity are associated with wider medians. However, no systematic relationship was found between the magnitudes of simple accident rates and median widths or setbacks to median trees. Estimates of simple accident rates show that overall accident rates for sections with median trees are in most situations significantly higher than overall rates for sections without trees. However, for most comparisons, the F& I accident rate differences are not statistically significant or are marginally significant. This result was found whether or not collisions occurring at intersections are included. The presence of median trees was also shown to be associated with statistically significant differences in collision characteristics. For most combinations of highway types, we observed increased proportions of hit object collisions and decreased proportions of head on and broadside collisions in the presence of median trees. While hit object collisions increase compared to other collision types, hit tree collisions increase relatively more, while other hit object types relatively decrease. There also exists an apparent association between median trees and the proportions of hit pedestrian collisions, especially for collisions not at intersections. All of the statistical analysis of this study involved cross sectional comparisons among similar groups of highway sections. No before after comparisons were made, although before after comparisons are recommended for future consideration, if found to be practical. Cross sectional models can give a general indication of what may occur if median trees are planted or removed at a particular site, if the site characteristics closely match the section data considered in the analysis. However, particular sites will always have unique features that limit the applicability of such models for prediction. The relationships developed in this report are not intended for predicting changes in collisions that might accompany some particular highway change. They were developed solely to determine whether or not significant statistical associations exist between collisions and the presence of median trees. An in depth investigation of about a hundred printed collision reports provided interesting and varied observations. The proportion of serious injuries and fatalities in collisions involving median trees appears about the same as in other hit object collisions in the sample. In just under half of the tree hit collisions examined, if the trees had not been present or had been cushioned in some manner, the resulting injuries would probably have been substantially 10 Although 95% can be said to be an arbitrary confidence level, it is widely regarded as an appropriate threshold in statistical investigations of this nature. 11 reduced. In about the same number of collisions, if the trees had not been present, the outcome may well have been more severe. The collision reports suggested no apparent linkage between the severity of hit tree collisions and median width. Some of the most serious tree hit collisions in the sample occurred on wide medians with substantial setback distances. Our investigation of differences between actual measured speeds and posted speeds on our selected highway sections revealed that although these measures are highly correlated, measured speeds ( for example, the 85% ile speeds) vary enough compared to posted speeds that, in an ideal world, measured speeds should be used in modeling. However, the data coverage for measured speeds is limited, affecting their ability to represent actual conditions on the highway. Consequently, using both measured speeds and posted speeds seems advisable. It was found that differences between the TASAS and SWITRS data used in the Phase II modeling lead to several kinds of biases in the collision counts obtained from these two data systems. However, these biases appear not to affect the ability of these models to estimate the associations between collisions and the presence of median trees. The findings of Phase II of this study are, on the whole, consistent with the findings presented in this report. The conclusions of the current study are more definitive due to the more in depth nature of the investigation. In summary, we find there is conclusive statistical and other evidence that median trees are associated with increased collisions, and increased collision severity. However, when considering only collisions located on the left side of the roadway, the linkages are weak. Nevertheless, there remains the expectation of increased collisions and greater severity of collisions in the presence of median trees. 1.4 Overview of the Rest of the Report The rest of this report contains four chapters and four appendices. Chapter 2 presents additional details concerning the development of the study data set used in the statistical analysis. Chapter 3 presents the detailed results from the statistical modeling work, including the presentation of simple accident rates and the specifications of the most statistically acceptable models relating collisions to highway characteristics. Chapter 4 presents the detailed findings of several additional investigations, including a review of selected original collision reports, an analysis of selected collision clusters, and comparisons of the suitability in modeling of posted speeds compared to measured speeds, and an assessment of differences in the TASAS and SWITRS data systems, conducted as a follow up to the Phase II report. Finally, Chapter 5 summarizes the principal conclusions and presents recommendations for additional investigations. The four appendices present summaries of the principal characteristics of the highway sections used in the analysis, as well as photos of these sections. 12 2. Development of the Phase III Data Set 2.1 Chapter Introduction This chapter describes the details of the data sets developed for the statistical analysis. It provides a full description of the sampling methodology, complete definitions of the variables used to represent highway characteristics, and information concerning the TASAS collision data that were used. 2.2 Sampling Considerations The data collection and modeling work previously conducted by this study, during Phase II, was based on a partial factorial design intended to ensure that enough field locations were included to provide an adequate amount of data to meet statistical accuracy targets. The accuracy targets were defined for accident rates stratified by the key physical features considered most likely to influence any relationship between collisions and median trees. This details of this factorial design are presented in the corresponding section of the Phase II report. 11 An analogous approach was taken to the data collection for Phase III, with a few changes motivated by experience from conducting the earlier parts of the study. The key variables used to guide the sampling of highway sections for the Phase III data collection are: Variations in posted speed, Variations in traffic volume ( ADT), Variations in median width, Variations in the setback from the median curb to median trees, Variations in assigned rate group. The last of these, rate groups, corresponds to the statewide categories by which California highway sections are grouped for the purpose of periodic reporting of accident rates and trends. A highway section is assigned to a particular rate group based on the type of highway, its surroundings, number of lanes, design speed, and in some cases the ADT. The basic goal of data collection is to ensure there are sufficient data collected for enough combinations of different levels of these key factors so the possible influence of these factors on collision frequency and severity can be determined. Note that, as in Phase II, posted speeds rather than measured speeds were used to guide the selection of study sections. This was for convenience since at the time the decisions regarding data collection were being made, data on measured speeds were not yet available. Actual measured speeds were used in the subsequent modeling and in the investigation reported in Section 4.4, which discusses the degree of correlation between posted speeds and actual speeds. Guided by the basic factorial design concepts discussed above and by the target level of exposure of 250 million vehicle miles, which is explained in detail in the Phase II report, our data collection effort was successful in adequately covering many of the factorial combinations that were targeted. Table 5 below shows the coverage of the data set with regard to three different categories of posted speeds and ADT. Table 6 shows the joint coverage of these two 11 Phase II Final Report. op cit. Section 2.3. 13 variables in combination. The cells show coverage of the data set measured in millions of vehicle miles ( MVM) of exposure. Table 5 shows that the data set has ample coverage for estimating the simple impacts on collisions of planting median trees, for different speeds and variations in ADT levels. The limited coverage for posted speeds of 50 mph and above is acceptable since these very high speed conventional highway sections are not of principal interest. The coverage for the lowest ADT category ( below 27,500 vehicles per day) is also limited, especially considering the absence of observations without median trees in that ADT range. However, we feel that the coverage in the medium to high ranges of ADTs is sufficient to examine the relationship between median trees and collisions across a sufficient range of ADT values. Table 5. MVM of Exposure by Posted Speeds, ADT, and Median Trees Median Type Median Type With Trees No Trees With Trees No Trees 30 35 1648 750 L 354 0 40 45 1424 1305 M 932 604 Posted Speed ( mph) 50+ 196 0 Average Daily Traffic H 1981 1451 Notes: 1. Low ADT is below 27,500, Medium is 27,500 to 40,000, and High is more than 40,000 vehicles per day in the year 2001. 2. MVM is section length times annual ADT times the number of days of accident data in each year, summed for highway sections with the stated characteristics and for the six years of coverage. 3. The target sample size is 250 MVM of exposure for each combination of characteristics. Table 6 shows that coverage is acceptable with regard to joint consideration of speeds and ADT. With the exception of sections with speeds 50 mph and above and in the low ADT category, there is ample coverage of other combinations of variables to estimate the main effects and their interactions. Clearly the effect of median trees can be determined with high statistical confidence for high ADT in both of the lower speed ranges and for median ADT in the 40 45 mph range. Table 6. MVM of Exposure by Posted Speeds Combined with ADT, and Median Trees Medians with Trees Medians without Trees Average Daily Traffic Average Daily Traffic L M H L M H 30 35 146 298 1204 0 0 750 40 45 126 521 777 0 604 702 Posted Speed ( mph) 50+ 82 114 0 0 0 0 Notes: 1. Low ADT is below 27,500, Medium is 27,500 to 40,000, and High is more than 40,000 vehicles per day in the year 2001. 2. The target sample size is 250 MVM of exposure for each combination of characteristics. 14 Similarly, Table 7 below shows the coverage of the data set with regard to different categories of median width and setback to median trees from the median curb. Table 8 shows the coverage of median width in combination with posted speeds. Table 9 shows the coverage for setback from the curb in combination with both posted speed and ADT. As before, each cell shows coverage measured in millions of vehicle miles ( MVM) of exposure for the given category. Table 7 shows that the data set provides good coverage for detecting the simple effect on collisions of having median trees across different median widths greater than 10 feet, and across different setback values with the exception of the very smallest (≤ 4 ft.). It is noteworthy that no state highways were found with median trees planted in medians less than 10 feet wide, even though many sections were found with setbacks to trees in the 4 6 foot range. Table 7. MVM of Exposure by Median Width and Setback to Median Trees Median Type Median Type With Trees No Trees With Trees No Trees 0 10 0 682 0 4 76 n/ a 10 16 2538 644 4 6 1679 n/ a Median Width ( feet) 16+ 729 728 6 8 1067 n/ a Setback: Curb to Med. Trees ( feet) 8+ 446 n/ a Note: 1. The target sample size is 250 MVM of exposure for each combination of characteristics. Table 8 shows that the data set permits many comparisons for medians 10 16 feet wide in both lower speed ranges, and for greater than 16 foot medians in the 40 45 mph range. As previously noted, comparing the effects of trees for 10 foot wide medians and less is not accommodated. Note that the coverage for 10 16 foot wide medians with trees in the 30 35 mph speed range is a little below the 250 MVM target threshold, but this is not a major deficiency. As before, we have a partial factorial design that provides opportunity to test relationships involving the major factors, as well as some second level interactions of interest. Table 8. MVM of Exposure by Median Width Combined with Speed, and Median Trees Medians with Trees Medians without Trees Posted Speed ( mph) Posted Speed ( mph) 30 35 40 45 50+ 30 35 40 45 50+ 0 10 0 0 0 532 150 0 10 16 1572 966 0 218 426 0 Median Width ( feet) 16+ 76 458 196 0 729 0 Note: 1. The target sample size is 250 MVM of exposure for each combination of characteristics. Table 9 shows a similar outcome with respect to coverage for testing the impacts on collisions of varying the setback between the median curb and median trees, for different posted speeds and ADT levels. Ample coverage exists for the 4 6 foot and 6 8 foot setback categories for both lower speed ranges, and also for the 8+ setbacks for the 40 45 mph range. Strong comparisons can also be made between the 4 6 foot and 6 8 foot setbacks for the high ADT range, between 15 the 6 8 foot and 8+ foot setbacks for the medium ADT range, as well as for variations in ADT within both the 4 6 foot and 6 8 foot setback categories. Table 9. MVM of Exposure by Speed and ADT Combined with Setback to Median Trees Medians with Trees Medians with Trees Posted Speed ( mph) Average Daily Traffic 30 35 40 45 50+ L M H 0 4 76 0 0 0 76 0 4 6 940 740 0 219 94 1367 6 8 632 352 82 135 317 615 Setback: Curb to Med. Trees ( feet) 8+ 0 332 114 0 446 0 Note: 1. The target sample size is 250 MVM of exposure for each combination of characteristics. Table 10 shows the breakdown with respect to coverage by rate group and median width. As previously noted, rate group is a code used by Caltrans to group highway sections for evaluating accident trends. The majority of sections in the data base are in rate groups H 38 and H 44, with two H 37s and just one H 43. The following table shows that coverage is sufficient to permit direct comparisons of the effects of median trees in the case of rate group H 38, for 10 16 foot medians, and for rate group H 44, for medians over 16 feet wide. In addition, we can compare collision experience between 10 16 foot and 16+ foot medians for both H 38 and H 44 highway sections, as well as between 0 10 foot and 16+ foot medians for H 44 highways. Table 10. MVM of Exposure by Rate Group Combined with Median Width, and Median Trees Medians with Trees Medians without Trees Median Width ( feet) Median Width ( feet) 0 10 10 16 16+ 0 10 10 16 16+ H 37 0 256 0 0 0 0 H 38 0 521 262 0 644 0 H 43 0 0 0 408 0 0 Rate Group H 44 0 1762 467 274 0 729 Note: 1. The target sample size is 250 MVM of exposure for each combination of characteristics. Finally, Table 11 below shows a similar breakdown including rate group and ADT category. Direct comparisons of the impacts of median trees on collision experience can be made for the H38 and H 44 rate groups, for both medium and high ADT ranges. ( Although coverage for the H 44 rate group in the medium ADT range is somewhat below the target, that will not seriously harm the comparison.) Similarly, the impact on collision experience for medians with and without trees can be compared between the medium and high ADT levels, for both the H 38 and H 44 highway types. 16 Table 11. MVM of Exposure by Rate Group Combined with ADT Category, and Median Trees Medians with Trees Medians without Trees Average Daily Traffic Average Daily Traffic L M H L M H H 37 146 110 0 0 0 0 H 38 73 395 315 0 426 218 H 43 0 0 0 0 0 408 Rate Group H 44 135 427 1667 0 177 825 Notes: 1. Low ADT is below 27,500, Medium is 27,500 to 40,000, and High is more than 40,000 vehicles per day in the year 2001. 2. The target sample size is 250 MVM of exposure for each combination of characteristics. To summarize, the above tables show that the twenty nine highway sections contained in the Phase III data set provide adequate coverage across many variations in the key variables. Initially, we were concerned that limiting the data collection to only state highways would make it difficult if not impossible to find a sufficient number of sections with median trees and combinations of narrow medians, narrow setbacks, and high speeds inconsistent with the side clearance standard found in the Caltrans Highway Design Manual. This turned out not to be as much of a problem as anticipated. Based on the information presented in this section, we believe the Phase III data set provides adequate coverage to support multivariate statistical modeling in order to explore the consequences of variations in these key variables. 2.3 Coding of Highway Section Characteristics The highway section characteristics used in Phase III of the study are mostly the same as were used in Phase II. The principal additions in Phase III are several parameters for measured speeds, and section rate group codes. The values for most characteristics were obtained through field measurements and from various published sources. The following is a detailed list of the section characteristics in the data set, providing details on coding methods and sources of information. Table 12. Coding of Highway Section Characteristics Characteristic Coding Method and Source of the Data Item Median Type Field Observation – Curbed w/ trees or Curbed – no trees Beginning & Ending Postmiles From CA Highway Log – A scale ( miles) for locating state highway features. The difference is the section length, if no postmile discontinuity occurs in the section. Posted Speed Field observation – Categorized as 30 35, 40 45, and 50+ mph. No sections have posted speeds under 30 mph. 50+ mph sections were excluded from most analyses. Average Speed From district speed studies, where available ( mph) – The average of any measured speeds in the section ( during or close to the 1996 2001 analysis period). 17 Characteristic Coding Method and Source of the Data Item 85% ile Speed From district speed studies – The average value below which 85% of the measured vehicle speeds fall ( also called “ critical speed”) Top of Pace Speed From district speed studies – The average top of the 10 mph speed range in which most measured speeds fall. % in Pace Range From district speed studies – The average % of measured speeds in the most observed 10 mph speed range. ( This estimates the variability of section speeds.) Bottom & Top of Pace % Range From district speed studies – The smallest and largest of the % in Pace Range values observed for the section. Section Length Calculated from postmile values ( in miles) Number of Lanes Field observation – The single direction lane count. Average Daily Traffic From: http:// www. dot. ca. gov/ hq/ traffops/ saferesr/ trafdata  Section values were interpolated/ extrapolated from the posted data for each year. Categorized as L (≤ 27,500), M ( 27,501 40,000), H(> 40,000) based on the year 2001. Total Median Width Field measurement – Curb to curb values. Categorized as 0 10, 10.1 16, 16.1+ feet. Median Shoulder Width Field measurement ( feet) – Stripe to curb. If no stripe, is estimated as total median lane width minus 12 feet. Distance – Curb to Median Trees Field measurement ( feet) – Categorized as 0 4, 4.1 6, 6.1 8, 8.1+ feet. Lane # 1 to Median Trees Sum of the previous two measurements – Categorized as 0 4, 4.1 6, 6.1 8, 8.1+ feet. Setback to Right Side Trees Field measurement ( feet) – Typical curb to tree distance. Median Curb Height Field measurement ( inches). Right Shoulder Width Field measurement ( feet) – Stripe to curb. If no stripe, is estimated as total right lane width minus 12 feet. Tree Trunk Diameter Field measurement – Typical median tree measured 4 feet above the ground ( feet). Right Side Curb Height Field measurement ( inches). Lane Widths (# 1 and RS Lanes) Field measurement ( feet) – Assumed 12 feet if no stripe. Million Vehicle Miles ( MVM) Calculated from section length and ADTs – Total estimated exposure for the six year ( 1996 2001) period. Nearby Land Use Field observation – Categorized as high, medium or low density commercial; high, medium or low density other Cross Street Density Field observation – Categorized as Low, Medium, or High density ( compared to other sections). 18 Characteristic Coding Method and Source of the Data Item Right Side Parking? Field observation – Categorized as Yes or No Right Side Trees? Field observation – Categorized as Yes or No Right Side Sidewalks? Field observation – Categorized as Yes or No Median Trees Aligned? Field observation – Categorized as Yes or No Highway Curvature Field observation – Categorized as L ( predominately straight), M ( gently curving), H ( tight curves), 90o turns Highway Grades Field observation – Categorized as L ( predominately level), M ( rolling, gentle grades), H ( steep grades) Ride Side Utility Poles Field observation – Categorized as Yes far from curb, Yes close to curb, or No Rate Group Determined from observed data, information in the California Highway Log, and design speed data from the Caltrans TASAS Unit, using definitions from the report 2001 Collision Data on California Highways. Expected Accident Rates ( Total and F& I) Average statewide accident rates for the rate group, obtained from 2001 Collision Data on California Highways The full data set used in the study is on line at http:// ceenve. calpoly. edu/ sullivan/ trees/. 2.4 Coding of Collision Data As previously mentioned, Phase II of this study used a data set containing a mix of state highway sections and sections under local jurisdiction. This was done in order to ensure having enough data with which to perform the statistical modeling. As a result, the data set for Phase II contained collision data from two sources: the California Highway Patrol ( CHP) maintained SWITRS data system for the local facilities, and the Caltrans maintained TASAS data system for the state highways. Concerns about possible incompatibilities between the two major state collision data systems led us to limit the Phase III investigation to state highway sections only. ( The experience of Phase II suggested it would be possible, after all, to find enough state highway sections to perform the statistical modeling, without having to fall back on local facilities to obtain enough pertinent observations.) The issue of incompatibilities between SWITRS and TASAS and how these might have affected the Phase II results is addressed in Section 4.5 of this report. In Phase III of the study, only state highway collision data from the TASAS system were used. Table 4 lists the data items extracted from TASAS for each highway section and included in the study data set. As noted, these data can be seen in their entirety in the study data set that is on line at http:// ceenve. calpoly. edu/ sullivan/ trees/. The overall data set contains a total of 228 different data items describing the number and characteristics of the collisions that occurred on each highway section. Unique column names were assigned to keep the information organized. Even so, the number of collision variables in combination with the 52 variables describing other section characteristics exceeded the 256 column capacity of Excel to store this information. For this reason, and for the sake of good organization, the Phase III data set consists of six Excel data files. They are: 19 1. The basic section characteristics ( see Section 2.3) combined with data for all the collisions occurring in each section during the 1996 2001 study period, regardless of location; 12 2. The basic section characteristics combined with collision data, omitting any collisions that occurred exclusively in the right lane, the right shoulder or beyond ( i. e., for which median characteristics can be assumed irrelevant); 3. The basic section characteristics combined with data for any collisions that involved the left ( median) shoulder, the median itself, or beyond ( i. e., for which median characteristics appear most relevant). 4. The same as data set # 1, except collisions within intersections are omitted. 5. The same as data set # 2, except collisions within intersections are omitted. 6. The same as data set # 3, except collisions within intersections are omitted. The first data set is called the “ Total Collisions – TC” file, the second the “ No Right Side – NRS” collisions file, the third the “ Left Side Only – LSO” collisions file, the fourth the “ Total Collisions No Intersctions – TCNI” file, the fifth the “ No Right Side No Intersections – NRSNI” file, and the sixth the “ Left Side Only No Intersections – LSONI” file. The collisions in each file are generally a subset of the file immediately above. Most of the Phase III modeling work utilized the second, third, fifth and sixth files, whereas the Phase II modeling work used a file similar to the first, although mainly including different highway sections. The highway section characteristics are duplicated in all files in order to faciltate working with each group of collisions independently. The processing to assign collisions to the various files examined fiveTASAS data fields – the “ Primary Location of Collision” field, three “ Other Location of Collision” fields, and the “ Intersection/ Ramp Location” field. The first four fields are coded separately for each party involved in the collision. For example, if a collision involved three vehicles, a total of twelve location fields were examined. Among the possible codes in these location fields, six were of principal interest: A – Beyond median or stripe ( left) B – Beyond shoulder driver’s left C – Left shoulder area F – Right lane G – Right shoulder area H – Beyond shoulder driver’s right If all the location fields for a collision contain only codes F, G, or H ( nothing else), that collision was excluded from the “ No Right Side” collision data sets; all other collisions being included. If any of the location fields for a collision contain A, B, or C, that collision was included in the “ Left Side Only” data sets; regardless of what other locations might also be coded. The following Intersection/ Ramp Location ( IRL) codes were of principal interest: 5 – Collision located within an intersection 6 – Collision located outside intersection, non state route 12 Collisions on intersecting cross streets, which also appear in TASAS, were omitted from all data sets. 20 Collisions with IRL = 6 were omitted from all six data sets while collisions with IRL = 5 were omitted from data sets 4 through 6. As noted, each file contains a very large number of collision counts, characterizing all the collisions in the group and just the collision involving fatalities and injuries ( F& I). Counts are further stratified by numerous collision characteristics, which are listed previously in Table 4. 21 3. Results from Modeling Based on TASAS Collision Data 3.1 Chapter Introduction This chapter presents the details of the statistical modeling. As described in Section 1.2, the modeling used three separate approaches: ( 1) testing several forms of generalized linear models, ( 2) estimating simple accident rates and confidence intervals, and ( 3) chi square testing of differences in collision characteristics. In all cases, the goal was to try to detect statistically significant differences in the collision estimates for highway sections with and without median trees. The possible effects of median trees were compared for many variations in the other highway characteristics listed in Table 2. The detailed findings are presented in the three sections that follow. The overall conclusion is that elusive but statistically significant associations exist between collision frequency and collision severity and the presence of median trees. However, these associations are weak when the frequency of Left Side Only collisions is considered. Collision frequency and severity are usually ( but not always) less for lower actual ( but not posted) speeds but, surprisingly, lower collision frequency and severity are associated with narrower medians. However, accident rate estimates indicate that differences in collision rates with and without median trees are largest for the lowest category of 85% ile speed considered. 3.2 Generalized Linear Modeling As described in Section 1.2, three different generalized linear model structures were tested with a large variety of candidate explanatory variables. Model GL 1: iXXMEDTREEADTLiERRCOLLiiiii)(... 25143210++++++= ββββββε ( this error term ERRi is assumed to follow the negative binomial distribution) Model GL 2: iXXMEDTREEiiiERRADTLCOLLiii)(... 231210++++= ββββε ( this error term ERRi is assumed to follow the Poisson distribution) Model GL 3: iXXMEDTREEALLiIFiERRCOLLCOLLiii)()(... & 231210++++= ββββε ( this error term ERRi is assumed to follow the Poisson distribution) Where: COLLi is the observed annual number of collisions on section i – in some models this is the annual collision count for a particular year, in others it is the six year average; Li is the section length ( miles); ADTi is the section average daily traffic; MEDTREEi is either 0 or 1, indicating whether section i has median trees; ε is the base of the natural logarithms (≈ 2.718); Xi1, Xi2, etc. are other section characteristics from Table 2; β0, β1, β2, etc. are parameters obtained from fitting the model to the data; 23 ERRi is an error term accounting for random effects not explicitly considered in the model. For each model tested, the statistical significance of the MEDTREEi variable was scrutinized to see if, in the presence of other variables, median trees appear to be significantly associated with the number of collisions ( in GL 1 and GL 2) or with the severity ratio ( in GL 3). Models GL 1 and GL 2 were tested for all collisions and for fatal and injury ( F& I) collisions alone, the latter being another indication of collision severity. As noted in Section 1.2, Model GL 1 is regarded as conceptually superior to Model GL 2 for representing collision frequency since it incorporates the section length and ADT variables in a more general manner. In an initial round of model testing, with intersection collisions included, each highway characteristic was examined by itself in addition to only the variables required in each basic model structure. The purpose of this was exploratory, to see under what circumstances, if any, the Medtree variable appeared to be statistically significant. In each case, the statistical significance of each included variable was given by its P value. If the P value for a given variable falls in the range 0 – 0.05, this indicates that the variable’s contribution to variations in the dependent variable ( the number of collisions or the severity ratio) is statistically significant at the 95% confidence level or better. If the P value is greater than 0.05, this indicates less confidence. For example, if P= 0.40, the corresponding variable would be judged significant at the 60% confidence level, which is quite insignificant. The tables below present most of the results of these initial model tests. Table 13 and Table 14 show results for models run using the “ No Right Side Collisions” data set, the first including all such collisions, the second including F& I collisions only. As noted, intersection collisions are included in all cases. Table 15 and Table 16 show the models run using the “ Left Side Only Collisions” data set. ( See Section 2.4 for the precise definitions of these two data sets.) In each case, the table shows, for each model type, the variables included and their corresponding P values, which indicate their statistical significance. 13 Cases where all variables are or are close to significant at the 95% level are highlighted. Models for which values are shown in bold and italics have all significant parameters and are discussed in further detail below. For convenience, in the GL 1 models, P values are omitted for the variable Li ( section length) because section length is always highly significant, usually with P values less than 0.0001. The models in the following tables generally are based on data for 23 of the 29 highway sections, omitting sections with 30 mph or 50 mph posted speeds, and in the H 37 or H 43 rate groups. This was done because sections with these characteristics either all have median trees 13 In an hypothesis test to test if a relationship exists ( such as between median trees and collisions), we assume that there is no relationship and then use our sample data to try to refute this assumption. Such tests are commonly conducted at the 5% level of significance, or, in the terminology of some researchers, the 95% level of confidence. In the tests conducted in this study, the P values for various tests are reported. Each P value is the probability of obtaining a value of our test statistic less likely than our observed value assuming no relationship between our response variable ( number of accidents, etc.) and the predictors ( medtree, posted speed, median width, etc.) If a P value is less than 0.05 ( 5%), the assumption of no relationship is viewed as very unlikely, and we conclude that a relationship between the variables exists at the 5% significance level ( the 95% confidence level). Essentially this says that the result we obtained would happen less than once out of 20 times if there was no relationship, so there is at most a 5% chance of making a mistake by concluding there is a relationship. When the test yields a P value greater than 0.05, the result tells us how far we would have to “ lower the bar” to conclude that the relationship exists. For example, if the P value were 0.15, one would have a 15% chance of making a mistake by concluding there is a relationship. In other words, the higher the P – value, the less evidence that there is a relationship, and the more evidence that there is no relationship. 24 or all do not have trees, therefore the effects of the median trees can not be discerned. ( Note that some test models were fit to the data for all 29 sections, with generally similar results.) Table 13. Significance of Initial Models for All “ No Right Side” Collisions Model GL 1 Model GL 2 Model Variable P Value ADTi P Value14 P Value 1 Medtree 0.104 0.003 0.013 2 Medtree 0.16 0.008 0.02 Posted Speed 0.35 0.89 2a Medtree 0.27 0.004 0.09 85% ile Speed 0.73 0.94 3 Medtree 0.15 0.0007 0.07 # 1 Lane Width 0.089 0.117 4 Medtree 0.11 0.0046 0.19 Rate Group 0.98 0.85 5 Medtree 0.268 0.01 0.02 MedWidthCat 0.577 0.84 6 Medtree 0.097 0.004 0.017 # lanes ( quan.) 0.63 0.53 7 Medtree 0.091 0.002 0.017 Curbheight 0.027 0.53 8 Medtree 0.057 0.003 0.024 X Street Density 0.169 0.95 9 Medtree 0.105 0.004 0.024 RS Parking 0.97 0.94 10 Medtree 0.067 0.0006 0.017 RS Sidewalks 0.036 0.324 11 Medtree 0.108 0.006 0.014 Curvature 0.84 0.72 12 Medtree 0.079 0.003 0.01 Grade 0.124 0.27 14 Since ADTi is in all GL 1 models, its P value appears in a separate column to make the table more compact. Li, which also is in all GL 1 models, has P values always less than 0.0001 and is not shown. 25 Model GL 1 Model GL 2 Model Variable P Value ADTi P Value14 P Value 13 Medtree 0.001 0.0006 0.005 LandUseCat15 0.0035 0.397 It should be noted that in the case of the GL 2 models a correction for over dispersion was necessary in order to obtain suitable estimates of the standard errors. Over dispersion in the uncorrected data presents a problem when the variance is much larger than the mean. The correction results in models that are consistent with their underlying assumptions, and leads to meaningful measures of significance ( P values). Patterns of residuals were also examined for the different model forms and judged to be consistent with the a priori assumptions about the error term distributions ( either negative binomial or Poisson, depending on the model). As seen above and in other tables below, very few of these simple models have statistically significant parameter values, that is, where all P values are less than 0.05. In Table 13, the presence of median trees is significant only for Model GL 2, where entered alone, and for Model GL 1 where entered with land use type. Model GL 1 was very close to significant if the presence of sidewalks is included, which also reflects the nature of the surrounding development. When only fatal and injury collisions are considered, the only simple relationship showing statistically significant parameters ( in Table 14) is Model GL 2, when the median width category is also included, and Model GL 1, when land use type is also included. When only the presence of median trees is included, both the GL 1 and GL 2 models are close to significant ( P values about .06). Medtree is not significant in any of the GL 3 models, in fact in most of these models the parameter estimates for Medtree= 0 are positive, implying greater severity where median trees are not present. Table 14. Significance of Initial Models for F& I “ No Right Side” Collisions Model GL 1 Model GL 2 Model GL 3 Model Variable P Value ADTi P Value P Value P Value 1 Medtree 0.068 0.0005 0.06 0.68 2 Medtree 0.16 0.008 0.072 0.73 Posted Speed 0.35 0.96 0.82 2a Medtree 0.25 0.002 0.08 0.53 85% ile Speed 0.46 0.56 0.20 3 Medtree 0.09 0.0001 0.20 0.73 # 1 Lane Width 0.038 0.19 0.95 4 Medtree 0.07 0.001 0.08 0.65 Rate Group 0.97 0.68 0.76 15 The model with land use is based on 22 highway sections rather than 23, since only one section with trees has the “ high commercial” land use, therefore no comparison for the effect of trees on collisions is possible for that land use category. 26 Model GL 1 Model GL 2 Model GL 3 Model Variable P Value ADTi P Value P Value P Value 5 Medtree 0.037 0.002 0.004 0.31 MedWidthCat 0.37 0.038 0.03 6 Medtree 0.05 0.002 0.11 0.77 # lanes ( categ.) 0.76 0.93 0.49 7 Medtree 0.063 0.0006 0.05 0.74 Curbheight 0.48 0.26 0.017 8 Medtree 0.027 0.0003 0.055 0.88 X Street Density 0.10 0.74 0.76 9 Medtree 0.068 0.001 0.06 0.86 RS Parking 0.80 0.67 0.53 10 Medtree 0.065 0.0003 0.06 0.79 RS Sidewalks 0.365 0.74 0.095 11 Medtree 0.098 0.0001 0.056 0.72 Curvature 0.47 0.57 0.75 12 Medtree 0.065 0.0006 0.073 0.52 Grade 0.71 0.74 0.096 13 Medtree 0.001 0.0001 0.0073 0.48 LandUseCat 0.006 0.273 0.31 Using the reduced LSO data set containing only the collisions that intrude into the median shoulder, the median, or beyond ( Table 15 and Table 16), the presence of median trees is shown to be mostly not significant. The exception is one of the F& I models in Table 16 where the combination of median trees and median width for Model GL 2 yields statistically significant parameters. Note that two sections without median trees have median width < 10 feet but there are no corresponding medians with trees in this category. If these two sections are excluded, the parameters of the GL 2 model become not significant ( P= 0.067 and 0.25 for Medtree and MedWidthCat, respectively). As before, the Medtree variable is consistently not significant ( by a wide margin) in the GL 3 severity models. Overall, it appears in these simple models with the Left Side Only data set that the influence of median trees is generally not significant. It should be noted, however, that with this data set the model fitting procedure was often unable to converge within the usual bounds; therefore results are ( at best) approximate. These P value estimates are based on approximate normal distributions of maximum likelihood estimators. 27 Table 15. Significance of Initial Models for All “ Left Side Only” Collisions Model GL 1 Model GL 2 Model Variable P Value ADTi P Value P Value 1 Medtree 0.38 0.019 0.094 2 Medtree 0.44 0.04 0.089 Posted Speed 0.58 0.66 2a Medtree 0.46 0.014 0.087 85% ile Speed 0.47 0.36 3 Medtree 0.47 0.005 0.33 # 1 Lane Width 0.13 0.087 4 Medtree 0.47 0.04 0.12 Rate Group 0.53 0.77 5 Medtree 0.55 0.075 0.07 MedWidthCat 0.57 0.49 6 Medtree 0.51 0.02 0.59 # lanes ( categ). 0.79 0.35 7 Medtree 0.38 0.02 0.10 Curbheight 0.94 0.99 8 Medtree 0.29 0.02 0.19 X Street Density 0.47 0.87 9 Medtree 0.39 0.039 0.08 RS Parking 0.57 0.59 10 Medtree 0.34 0.005 0.116 RS Sidewalks 0.034 0.365 11 Medtree 0.37 0.01 0.135 Curvature 0.29 0.182 12 Medtree 0.29 0.02 0.066 Grade 0.056 0.20 13 Medtree 0.11 0.018 0.06 LandUseCat 0.26 0.86 28 Table 16. Significance of Initial Models for F& I “ Left Side Only” Collisions Model GL 1 Model GL 2 Model GL 3 Model Variable P Value ADTi P Value P Value P Value 1 Medtree 0.87 0.03 0.44 0.27 2 Medtree 0.81 0.028 0.35 0.31 Posted Speed 0.67 0.43 0.48 2a Medtree 0.84 0.03 0.11 85% ile Speed 0.77 0.78 3 Medtree 0.99 0.009 0.98 0.40 # 1 Lane Width 0.10 0.05 0.38 4 Medtree 0.97 0.07 0.49 0.27 Rate Group 0.56 0.74 0.83 5 Medtree 0.53 0.06 0.06 0.97 MedWidthCat 0.25 0.05 0.06 6 Medtree 0.88 0.07 0.47 0.30 # lanes ( quant.) 0.96 0.76 0.58 7 Medtree 0.76 0.028 0.34 0.16 Curbheight 0.076 0.085 0.002 8 Medtree 0.68 0.05 0.49 0.47 X Street Density 0.45 0.85 0.89 9 Medtree 0.87 0.156 0.28 0.40 RS Parking 0.17 0.30 0.38 10 Medtree 0.85 0.02 0.44 0.36 RS Sidewalks 0.45 0.87 0.12 11 Medtree 0.88 0.026 0.51 0.33 Curvature 0.49 0.48 0.51 12 Medtree 0.86 0.036 0.45 0.14 Grade 0.56 0.94 0.08 13 Medtree 0.31 0.019 0.17 0.17 LandUseCat 0.13 0.94 0.28 This initial exploratory modeling produced mixed results. There is no consistent evidence that the presence of median trees is systematically associated with more collisions or greater collision severity. On the other hand, especially using the larger data set ( which excludes only the right side collisions), some significant associations are evident. When the data set is limited to left side collisions, there appears no strong statistical evidence that the number or the severity of collisions are associated with the presence of median trees. 29 On the other hand, in these simple model forms, the effects of median trees may be hidden by associations between collisions and combinations of other section characteristics that need to be controlled for in order for the effects of median trees to become visible. This can be especially true if the association between collisions and median trees is weak compared to the influence of the other variables. For this reason, in depth multivariate modeling was performed. Based on logic and insights gained from the preceding analysis of simple model forms, a “ short list” of candidate predictor variables was postulated. This showed some of the candidate variables having little statistical association with collisions. A pruning procedure was then followed through which the least significant predictors, except for Medtree, were eliminated. The pruning continued until all of the variables remaining in the model were significant, or almost so. The final set of candidate predictor variables for the multivariate models is the following: Medtree – Median Trees Present ( Yes, No) Speed ( both posted speed – 35, 40, 45 – and 85% ile speed – 40, 45, 50 – were tested) Median Lane Width (# 1 Lane) Rate Group ( H 38 or H 44) Median Width Category ( 10 16 or > 16 ) Median Curb Height Number of Lanes ( either 2, 3, 4, or 2, 3& 4, coded as a categorical variable) Cross Street Density ( L, M, H) Right Side Sidewalks ( Yes, No) Land Use Type ( Commercial, Other) As previously noted, the amount of variation in some variables was limited by the data set. For example, all 30 mph speed sections had median trees, therefore these 30 mph sections were not included due to the lack of directly comparable sections without median trees. The three model forms ( GL 1, GL 2, GL 3) were tested for four data sets ( NRS – “ No Right Side,” LSO – “ Left Side Only,” NRSNI – “ No Right Side No Intersections,” and LSONI – “ Left Side Only No Intersections”) and the GL 1 and GL 2 forms were tested for all collisions and for F& I collisions separately. Most of these tests produced models with some parameters, often including the Medtree parameter, not statistically significant. Selected results of the multivariate model tests are summarized in Table 17 and Table 18 below. Although most models that fit the data poorly are not shown, a number are shown below for comparison with models with similar specifications that fit the data well. Models in which all the parameters are statistically significant ( or close) are highlighted in bold italics. Most of these are subsequently discussed in detail. In cases of parameter values “ close” to significant, two levels are identified – parameters significant at the 90 95% confidence level are coded “ C1,” while parameters significant at the 80 90% level are coded “ C2.” In comparing the models in Table 17 and Table 18, a few noteworthy patterns are evident. First, it is clear that the three basic model forms usually give very different results for the same combination of variables. That GL 3 performs very differently from GL 1 and GL 2 is expected, since GL 3 models severity, while the others model collision frequency, although in different ways. GL 1 is conceptually superior to GL 2 since it provides more flexibility in modeling the influence on collisions of different section lengths and ADTs. Although different, the GL 1 and GL 2 models for a given specification often show quite a bit of similarity in their outcomes. 30 Usually, the models fit to the data sets that exclude intersection collisions are similar to the models that include these collisions. However, their statistical properties are somewhat stronger. On the other hand, achieving model convergence proved more difficult for the smaller non intersection collision data sets, especially for the smallest LSONI data set. Another noteworthy factor is that substituting 85% ile speed for posted speed, all other factors being equal, generally produces different results. However, in some cases, these differences are small. This indicates that even though posted speeds and actual measured speeds are highly correlated ( see Section 4.4), they are not equivalent for statistical modeling. ( As discussed in Section 4.4, both speed measurements have certain practical limitations, so it is difficult to know whether one is better than the other. Consequently, we considered both. A final observation about these alternative multivariate models is the degree of volatility observed in fitting the models to the different data sets. Adding or eliminating one variable typically caused large changes in parameter values, and corresponding levels of significance. In part, this volatility is due to the relatively small data sets used, even though nearly all suitable and comparable highway sections in the State of California were included. In part, the volatility may be due to the diversity and random nature of the collisions themselves. Also, collision causes are complex and varied, and simple general explanations simply are not possible. The “ best” of the models identified in Table 17 and Table 18 are discussed in detail below. Table 17. Summary of Multivariate Models with Intersection Collisions Included Significance of Included Optional Variables ( See Note Below) Model Form ( GL?) Dataset Used Collisions Included Posted Speed 85% ile Speed Median Width # 1 Lane Width Median Curb Ht. Land Use Sidewalks X St. Density No. of Lanes Rate Group All Pars. Significant? Medtree P Value 1 NRS All C2 S C .02 1 NRS All N C1 S N N N .03 1 NRS All C2 S S C2 N N .02 1 NRS F& I C2 C1 C1 C1 C .002 1 NRS F& I C2 S C1 C .01 1 NRS F& I C1 S S C .07 1 NRS F& I C2 S N S N N N .14 1 NRS F& I N S C2 S C2 C2 N .13 1 NRS F& I S N S S C1 N .01 1 NRS F& I S N C1 S S N .07 1 LSO All S S S N N Q .44 1 LSO All N N N N .66 1 LSO F& I N N C2 N .04 2 NRS All S S S S S Y .01 2 NRS All N S C1 N N N .06 31 Significance of Included Optional Variables ( See Note Below) Model Form ( GL?) Dataset Used Collisions Included Posted Speed 85% ile Speed Median Width # 1 Lane Width Median Curb Ht. Land Use Sidewalks X St. Density No. of Lanes Rate Group All Pars. Significant? Medtree P Value 2 NRS All C2 N N .05 2 NRS F& I S S S S S S Y .01 2 NRS F& I N S C2 C1 N N N .19 2 NRS F& I C2 C1 C1 C1 N N .02 2 NRS F& I S N N N N .01 2 NRS F& I N N N N N N .10 2 NRS F& I C1 N N N .02 2 NRS F& I N C1 C2 N .24 2 LSO All S S S S C .12 2 LSO All N N N N .49 2 LSO F& I N C2 N N .08 3 NRS  C1 N N N N N .25 3 NRS  N N N N N N .66 3 NRS  C2 N N N N N N .. 31 3 NRS  N N C2 N N N N .76 3 NRS  N S N N N N .11 3 NRS  S N N C2 N .15 3 NRS  N N N .78 3 NRS  S N C2 N .14 3 NRS  N N N N .58 3 LSO  C1 S S C .02 3 LSO  N S N .31 3 LSO  S C1 C .12 3 LSO  C2 S N S N .04 3 LSO  N C1 N N N Q .89 Notes: 1. The statistical significance of each model parameter is coded as follows: S – Parameter is significant at the 95% confidence level, C1 – Parameter is significant at the 90 95% confidence level, C2 – Parameter is significant at the 80 90% confidence level, N – Parameter is not significant ( i. e., significance is less than the 80% level). 32 2. The next to last column showing the significance of all model parameters is coded as: Y – All model parameters are significant at the 95% level, C – All model parameters are acceptable ( all coded S, C1 or C2), N – At least one model parameter is not statistically significant, N Q – Parameters are not significant and the model did not converge normally. Table 18. Summary of Multivariate Models with Intersection Collisions Excluded Significance of Included Optional Variables ( See Note Below) Model Form ( GL?) Dataset Used Collisions Included Posted Speed 85% ile Speed Median Width # 1 Lane Width Median Curb Ht. Land Use Sidewalks Average ADT No. of Lanes Rate Group All Pars. Significant? Medtree P Value 1 NRSNI All S S S S S Y .02 1 NRSNI All C2 S S S S C .01 1 NRSNI All C2 S S S S C .02 1 NRSNI All C1 S S S C .03 1 NRSNI All N S S S S C1 N .004 3 NRSNI  S S C2 C1 C .06 3 NRSNI  S S C1 S C .03 3 NRSNI  S C1 N N .28 3 NRSNI  S C2 N .49 3 NRSNI  S S N N S N .13 3 NRSNI  S S C1 N .22 3 LSONI  S Y .04 3 LSONI  C1 S N N .31 3 LSONI  C2 S N .44 3 LSONI  S C2 N N .65 3 LSONI  S C1 N .40 3 LSONI  S N .72 See notes for Table 17. The following provides further detail and discussion about selected multivariate models for which all parameters are statistically significant at the 95% level ( or close). The Best Models of Type GL 1 Only one of the GL 1 models tested has parameters that are all significant at the 95% level, but seven other models came close. All were developed using the No Right Side collisions data sets. These models are highlighted in the tables above. None of the GL 1 models developed 33 using the Left Side Only data sets gave acceptable statistical properties. Of all the candidate variables tested, the # 1 ( median) lane width and the surrounding land use were most often linked with the number of collisions. Median curb height appears in four models, a speed variable appears in three, and median width appears in two of the models. The first and simplest GL 1 model appears below in Table 19. It was estimated using the data set containing all of the No Right Side collisions and includes intersection collisions.. Table 19. Multivariate Model GL 1 A Estimated for NRS ALL Collisions Data Points ( N): 23 Degrees of Freedom ( DF): 17 Variable Estimate Standard Error P Value Intercept . 0965 1.3595  Section Length 0.3578 0.0415 < 0.0001 Average ADT 0.2694 0.0691 0.0005 Medtree = 0  0.3393 0.1430 0.024 Median Lane Width 0.1695 0.1032 0.109 Land Use = Commercial 0.3959 0.1373 0.008 The following statistics appear in the table: The degrees of freedom ( DF) are the number of data points ( 22) minus the number of estimated parameters ( 10). The Standard Error measures the amount of variation in each parameter estimate. The P value measures the statistical significance of each parameter’s contribution to the model, with smaller being better. Values under 0.05 indicate significance at the 95% confidence level. Many variables in these models are categorical, where one category is selected as the base. For example, in the above model, the base categories for the categorical variables are Medtree= 1 and LandUse= Other. ( SectionLength, AverageADT, and MedianLaneWidth are continuous variables.) Each categorical parameter estimate shows the effect of the indicated category relative to the base. For example, in the above model, the effect on collisions of Medtree= 0 ( no median trees) is negative ( i. e., fewer collisions are expected) while the effect on collisions of commercial land use is positive ( i. e., more collisions are expected than for other land uses). Therefore, the model suggests that highway sections with median trees are expected to have more collisions than sections without trees, when the effects of section length, ADT, median lane width, and surrounding land use are controlled for. The model also suggests that the number of collisions increases with ADT but much less than proportionally. Specifically, in this version of Model GL 1: iADTiCOLL0.2694ε≈ Thus, the model implies that if ADT doubles and everything else remains the same, the number of collisions would increase by a factor of 2694.0) 2694.0)( 2(/ εε or 1.3. This is not unreasonable. On the other hand, if the section length doubles, with everything else the same, collisions would 34 increase by a factor of 1.43. On face, this may not seem reasonable. 16 In general, one would not want to use a model of this type for accident prediction. However, the model does show that there is a statistically significant association between median trees and the total number of NRS collisions. It also suggests that the number of collisions is positively associated with increasing median lane width. ( This relationship is also observed in the simple accident rate models presented later in Section 3.3.) Note however that the median lane width variable is not quite significant at the 95% level. The one model that was found in which all parameters are significant at the 95% level was estimated using the data for all No Right Side collisions, with collisions at intersections excluded. This model appears in Table 20 below. Table 20. Multivariate Model GL 1 B Estimated for NRSNI ALL Collisions Data Points ( N): 22 Degrees of Freedom ( DF): 14 Variable Estimate Standard Error P Value Intercept  2.2582 1.1445  Section Length 0.3532 0.0321 < 0.0001 Average ADT 0.3479 0.0622 < 0.0001 Medtree = 0  0.2983 0.1192 0.019 # Lanes = 2 0.2760 0.1200 0.035 Median Curb Height 0.0716 0.0265 0.011 Median Lane Width 0.2453 0.0831 0.009 Land Use = Commercial 0.3940 0.1119 0.003 On the whole, there is considerable consistency in the parameters that are common to the above two models. This new model implies that sections without median trees in our sample have times the total non intersection collisions compared to sections with median trees, when differences due to section length, ADT, number of lanes, # 1 lane width, curb height, and land use are separately accounted for. Note that the number of lanes enters as a category variable, with directional two lane sections associated with more collisions than the alternative base case, which is three or four directional lanes. Median curb height enters this model with a positive parameter value, meaning that, in this data set, higher median curbs are associated with more collisions, everything else being equal. 74.02983.0=− ε In neither of these initial models did variables measuring median widths or speeds enter as being even close to statistically significant. In fact, median width was never found significant in 16 A peer reviewer comments that it may “ not seem reasonable if you think that twice the length should be twice the accidents. However, section length in the database is often determined by the distance between major intersections ( where ADT may change). Therefore, section length is associated with intersection density and other variables. For this reason ( when access, either by intersections or by driveways and commercial access is not accounted for) L is a proxy for all these variables. Because more than half of all accidents are intersection and access related, not having these variables in the model will generally produce strange results. In particular, you will not know whether what you attribute to median trees really reflects an association between these and access density.” 35 any of the GL 1 models based on all No Right Side collisions. However, median width did enter into two models fit to No Right Side fatal and injury ( F& I) collisions, as seen later in this section. Two models based on all No Right Side collisions, excluding intersections, were found to have speed variables close to statistically significant. These appear below in Table 21 and Table 22. Table 21. Multivariate Model GL 1 C Estimated for NRSNI ALL Collisions Data Points ( N): 22 Degrees of Freedom ( DF): 13 Variable Estimate Standard Error P Value Intercept  2.1026 1.2187  Section Length 0.3598 0.0384 < 0.0001 Average ADT 0.3010 0.0644 < 0.0001 Medtree = 0  0.3950 0.1458 0.009 85% ile Speed = 40  0.3984 0.1931 0.124 85% ile Speed = 45  0.1617 0.1522 0.124 Median Curb Height 0.0675 0.0283 0.021 Median Lane Width 0.2638 0.0924 0.009 Land Use = Commercial 0.5726 0.1449 0.001 Table 22. Multivariate Model GL 1 D Estimated for NRSNI ALL Collisions Data Points ( N): 22 Degrees of Freedom ( DF): 13 Variable Estimate Standard Error P Value Intercept  1.3999 1.2099  Section Length 0.3479 0.0364 < 0.0001 Average ADT 0.3220 0.0651 < 0.0001 Medtree = 0  0.3673 0.1454 0.015 Posted Speed = 35  0.1005 0.1840 0.143 Posted Speed = 40  0.2853 0.1661 0.143 Median Curb Height 0.0619 0.0293 0.042 Median Lane Width 0.2078 0.0904 0.029 Land Use = Commercial 0.4201 0.1272 0.005 As before, there is considerable consistency in the model parameters common to the other models. The new speed variables ( 85% ile and posted speed) both enter as category variables with the highest speed used as the base. For 85% ile speed, the category “= 40” covers sections in the 35 40 mph 85% ile speed range, while “= 45” covers sections in the 40 45 mph range. This model indicates that lower 85% ile speeds are associated with fewer collisions, compared to the base case of speeds above 45 mph. The second model, which includes posted speed, is less straightforward. Here, 40 mph posted speed is associated with the fewest collisions, and 35 mph has the second fewest, compared to 36 the base case of 45 mph posted speed. On the other hand, the standard errors suggest that the difference between 35 mph and 40 mph posted speeds is not statistically significant. Three other GL 1 models with reasonable statistical properties were estimated using the data set for No Right Side fatal and injury ( F& I) collisions, including intersection collisions. The first of these appears in Table 23 below. Note that no acceptable models could be found for the NRSNI F& I data set with intersection collisions excluded. Table 23. Multivariate Model GL 1 E Estimated for NRS F& I Collisions Data Points ( N): 21 Degrees of Freedom ( DF): 13 Variable Estimate Standard Error P Value Intercept  1.1616 1.3767  Section Length 0.3540 0.0390 < 0.0001 Average ADT 0.3394 0.0838 0.0004 Medtree = 0  0.5913 0.1760 0.0022 Median Width = 10 16  0.2822 0.1694 0.127 Median Lane Width 0.1859 0.1017 0.071 # Lanes = 2 0.3201 0.1657 0.065 Land Use = Commercial 0.2830 0.1472 0.065 This model introduces a new categorical variable for median width. The base value for this variable is Median Width = 16+. Since there are no sections in the data with median widths less than 10 feet and trees, the 0 10 foot median width category was excluded from this estimation. This model is weak statistically in that only a few variables ( section length, ADT, and median trees) are significant at the 95% level. The implications of the model are similar to the model described previously for variables they have in common ( except, of course, this model applies to F& I collisions). In addition, the model implies that roadways with 10 16 foot medians have fewer F& I collisions than medians wider than 16 feet. This seems counter intuitive, but it should be noticed that the median width variable has low statistical significance. The second GL 1 model for No Right Side fatal and injury ( F& I) collisions incorporates 85% ile speed. It appears in Table 24 below. The categorical 85% ile speed variable is defined as before. The apparent association in this model between collisions and speed is hump shaped – where the 35 40 mph category has the fewest collisions, 40 45 mph has the most, and 45 50 mph is in the middle. The contributions of other variables are the same as in previous models. Note that, in this model, the presence of median trees is not quite significant at the 95% level, nor is the 85% ile speed. Table 24. Multivariate Model GL 1 F Estimated for NRS F& I Collisions Data Points ( N): 22 Degrees of Freedom ( DF): 14 Variable Estimate Standard Error P Value Intercept  1.4274 1.2760  Section Length 0.3127 0.0353 < 0.0001 Average ADT 0.2367 0.0667 0.0004 Medtree = 0  0.2667 0.1496 0.072 37 85% ile Speed = 40  0.1937 0.1985 0.054 85% ile Speed = 45 0.2515 0.1535 0.054 Median Lane Width 0.2288 0.0975 0.018 Land Use = Commercial 0.4260 0.1447 0.007 The final GL 1 model estimated using No Right Side fatal and injury ( F& I) collision data is shown in Table 25 below. Table 25. Multivariate Model GL 1 G Estimated for NRS F& I Collisions Data Points ( N): 21 Degrees of Freedom ( DF): 14 Variable Estimate Standard Error P Value Intercept  1.7693 1.4873  Section Length 0.3339 0.0418 < 0.0001 Average ADT 0.4033 0.0859 < 0.0001 Medtree = 0  0.5307 0.1865 0.008 Median Width = 10 16  0.2768 0.1844 0.157 Median Lane Width 0.2321 0.1096 0.040 # Lanes = 2 0.3440 0.1777 0.063 This is the same specification as model GL 1 E ( Table 23) except that land use is not included. As in the previous model, the median width variable has poor statistical significance. The associations are basically the same as the other GL 1 models described in this section. In summary, only eight of the dozens of GL 1 models tested showed acceptable or near acceptable statistical properties. Seven of these are shown in detail above. These models generally seem logical, and all show that there is an association between median trees and an increased number of either total collisions or F& I collisions when the No Right Side data sets are used. Removing collisions that occur at intersections does not appear to affect the results very much. A counter intuitive aspect found in two of the models is that the increase in collisions from having median trees is not mitigated by increased median width. However, it should be noted that data limitations did not permit modeling medians narrower than 10 feet. The possible mitigating aspects of lower section speed were found to be mixed. Finally, it is noteworthy that, despite numerous efforts, no statistically significant associations of the GL 1 model form were found using the data for Left Side Only collisions. The Best Models of Type GL 2 Three GL 2 models were found to with acceptable statistical properties. In two of these, all parameters are significant at the 95% level. In the other, all parameters are significant except for the presence of median trees, which is close to significant. Curiously the three acceptable models were estimated on three different data sets – one each for all No Right Side collisions, F& I No Right Side collisions, and all Left Side Only collisions. No model with acceptable properties could be found using only F& I collisions in the Left Side Only data set. For the sake of comparison, the best model found for the F& I Left Side Only collisions is described, even 38 though the presence of median trees is not significant in this model. Collisions at intersections are included in all the data sets used to fit the GL 2 type models. Cross street density and Land Use appear as significant variables in all three of the models. The number of lanes and posted speed, as well as median curb height appear in two. Median width entered only one model as a significant variable. 85% ile speed was found never to have a significant association in any of the GL 2 models tested. The first GL 2 model appears below in Table 26. It was estimated using the data for all of the No Right Side collisions. All of the categorical variables have been discussed previously, except Cross Street Density, for which the base category is Cross Street Density = M ( medium). In this model, 3 lane and 4 lane directional segments were categorized separately, with # Lanes = 4 used as the base. Table 26. Multivariate Model GL 2 A Estimated for NRS ALL Collisions Data Points ( N): 22 Degrees of Freedom ( DF): 12 Variable Estimate Standard Error P Value Intercept  2.2090 1.2493  Medtree = 0  0.5191 0.1743 0.011 Posted Speed = 35 0.3233 0.1994 0.024 Posted Speed = 40  0.1727 0.1878 “ Cross Street Density = H  0.3541 0.1971 0.015 Cross Street Density = L 0.6584 0.1932 “ Median Lane Width 0.2896 0.1032 0.017 Land Use = Commercial 0.4582 0.1429 0.007 # Lanes = 2  0.5777 0.2521 0.053 # Lanes = 3  0.9584 0.3520 “ As previously noted, the GL 2 models are mathematically equivalent to multinomial models of accident rates. The above model indicates that the accident rate for all No Right Side collisions is higher for sections with median trees ( since the parameter value for Medtree= 0 is negative). The model also implies a U shaped relationship between the accident rate and posted speed – greatest for 35 mph, least for 40 mph, and greater again for 45 mph ( but still below the rate for 35 mph). This is exactly the opposite relationship to that found in one of the GL 1 models. The relationship with cross street density implies that accident rates decrease with increasing cross street density, which is counter intuitive because collisions are known to concentrate at intersections. The roadway width effect is different than found previously – here, three lane directional roadways are associated with the lowest accident rates, followed by two lane roadways, with four lane roadways associated with the highest accident rates. The second GL 2 model, based on F& I No Right Side collisions, is shown below in Table 27. The effects of the different parameters in this model for F& I collisions are mostly similar to the previous model for all collisions ( Table 26). However, the variable for median curb height enters this model and indicates that higher median curbs are associated with fewer collisions, which is the opposite effect found in some of the GL 1 type models. The effect of posted speed changes from U shaped to monotonic, indicating that collisions decrease as section posted speeds 39 increase from 35 to 45 mph. In both models, the highest accident rates are associated with the lowest posted speed category, 35 mph. Table 27. Multivariate Model GL 2 B Estimated for NRS F& I Collisions Data Points ( N): 22 Degrees of Freedom ( DF): 11 Variable Estimate Standard Error P Value Intercept  3.8998 0.9956  Medtree = 0  0.4717 0.1449 0.008 Posted Speed = 35 0.7074 0.1694 0.001 Posted Speed = 40 0.1483 0.1740 “ Cross Street Density = H  0.5217 0.1688 0.001 Cross Street Density = L 0.8404 0.1552 “ Median Lane Width 0.3877 0.0832 0.001 Median Curb Height  0.0637 0.0234 0.017 Land Use = Commercial 0.5049 0.1243 0.002 # Lanes = 2  0.6606 0.2066 0.003 # Lanes = 3  1.3091 0.2967 “ The third GL 2 model with acceptable statistical properties is shown below in Table 28. In this model, estimated for all Left Side Only collisions, the influence of median trees is not statistically significant at the 95% level, although it is close. Other parameters are statistically significant at the 95% level. In this case, the model implies that the accident rate for median width 10 16 feet is higher than for the wider medians. ( This is the opposite of what the GL 1 models indicate.) The implications of other variables are the same as in the previous models. Table 28. Multivariate Model GL 2 C Estimated for LSO ALL Collisions Data Points ( N): 20 Degrees of Freedom ( DF): 13 Variable Estimate Standard Error P Value Intercept  0.6992 0.2302  Medtree = 0  0.2664 0.1598 0.117 Cross Street Density = H  0.2443 0.1592 0.013 Cross Street Density = L 0.5603 0.1941 “ Median Width Cat. = 10 16 0.4689 0.1987 0.035 Land Use = Commercial 0.4528 0.1667 0.017 Median Curb Height  0.1168 0.0460 0.022 Finally, for comparison, Table 29 shows the result of the best GL 2 model estimated using the F& I Left Side Only collisions. Although median lane width and median curb height are close to being significant at the 95% level, the presence of median trees is not at all significant ( P= 0.92). Eliminating the other variables one by one does not change this outcome. 40 Table 29. Multivariate Model GL 2 D Estimated for LSO F& I Collisions Data Points ( N): 22 Degrees of Freedom ( DF): 18 Variable Estimate Standard Error P Value Intercept  4.0240 1.6177  Medtree = 0  0.0171 0.1675 0.920 Median Lane Width 0.2560 0.1369 0.083 Median Curb Height  0.0815 0.0392 0.051 The overall conclusion from the GL 2 modeling is that there is an association between accident rates and the presence of median trees, when all Not Right Side collisions are considered. If the analysis is limited to Left Side Only collisions, a weak association remains between collisions and the presence of median trees ( the presence of median trees is significant at the 80% confidence level). Neither posted speed nor 85% ile speed was found to be significant for “ Left Side Only” collisions. Although posted speed enters as a significant variable for No Right Side collisions, its effect is counter intuitive, slower speeds being associated with more collisions. The Best Models of Type GL 3 Model type GL 3 addresses collision severity by considering the proportion of F& I collisions on the highway sections. Many different model specifications were tested, some of which are shown in Table 17 and Table 18. Three models with acceptable statistical properties were found using data sets that exclude collisions at intersections; while only one acceptable GL 3 model was found when intersection collisions are included. This last model, estimated for Left Side Only collisions, appears in Table 30 below. Table 30. Multivariate Model GL 3 A Estimated for LSO Collisions Data Points ( N): 20 Degrees of Freedom ( DF): 13 Variable Estimate Standard Error P Value Intercept  0.2119 0.1407  Medtree = 0  0.2723 0.0985 0.017 Median Width = 10 16  0.4115 0.0868 0.0005 Cross Street Density = H 0.0246 0.0817 0.014 Cross Street Density = L  0.2924 0.0 



B 

C 

I 

S 


